Let S n be a symmetric simple random walk on the integer lattice Z d . For a Bernstein function ϕ we consider a random walk S n ϕ which is subordinated to S n . Under a certain assumption on the behaviour of ϕ at zero we establish global estimates for the transition probabilities of the random walk S n ϕ . The main tools that we apply are a parabolic Harnack inequality and appropriate bounds for the

The main focus of this paper is on study of s‐numbers for a higher order Sobolev embedding on an interval and also for the corresponding Hardy‐type operator. Upper and lower estimates for approximation and Bernstein numbers are described and their relations with results for lower order Sobolev embeddings are discussed.

In this paper, we investigate the Hausdorff dimension of the invariant measures of the iterated function system (IFS) { α x , β x , γ x + ( 1 − γ ) } . We provide an “almost every” type result by a direct application of the results of Feng and Hu [5] and Kamalutdinov and Tetenov [9].

We provide a study of Köthe sequence algebras. These are Fréchet sequence algebras which can be viewed as abstract analogoues of algebras of smooth or holomorphic functions. Of particular treatment are the following properties: unitality, m‐convexity, Q‐property and variants of amenability. These properties are then checked against the topological ( DN ) ‐(Ω) type conditions of Vogt–Zaharjuta. Description

In this paper, we discuss a diffusive predator‐prey model with predator cannibalism in spatially heterogeneous environments. In contrast with spatially homogeneous environments, we find the dynamics of the model in spatially heterogenous environments is more complicated. For the spatially heterogeneous case, we could classify death rate of the predator into four different regions and demonstrate that

In this paper we consider laminated beams modelled from the well established Timoshenko system, which is a structure given by two identical layers uniform on top of each other, taking into account that an adhesive of small thickness is bonding the two surfaces and produces an interfacial slip. By using semi‐group approach, we prove the global well‐posedness of the system when a viscoelastic dissipation

We study a class of nonlinear elliptic equations involving measure data − div A ( x , D u ) = μ in Ω , where μ is a Radon measure. Under the main assumption of A ( x , ξ ) that there exists a constant Λ > 0 such that | A ( x , ξ ) − A ( x 0 , ξ ) | ≤ Λ ( a ( x ) + a ( x 0 ) ) | x − x 0 | α ( | ξ | 2 + s 2 ) p − 1 2 , α ∈ ( 0 , 1 ] , where 0 ≤ a ( x ) ∈ L m ( Ω ) for some integrable index m > 1 , we

We prove L p estimates, 1 ≤ p ≤ ∞ , for solutions to the tangential Cauchy–Riemann equations ∂ ¯ b u = ϕ on a class of infinite type domains Ω ⊂ C 2 . The domains under consideration are a class of convex ellipsoids, and we show that if ϕ is a ∂ ¯ b ‐closed (0,1)‐form with coefficients in L p , then there exists an explicit solution u satisfying ∥ u ∥ L p ( b Ω ) ≤ C ∥ ϕ ∥ L p ( b Ω ) . Moreover, when

We study the existence of a time‐periodic solution with pointwise decay properties to the Navier–Stokes equation in the whole space. We show that if the time‐periodic external force is sufficiently small in an appropriate sense, then there exists a time‐periodic solution { u , p } of the Navier–Stokes equation such that | ∇ j u ( t , x ) | = O ( | x | 1 − n − j ) and | ∇ j p ( t , x ) | = O ( | x |

In the paper we prove that the Nevanlinna counting function and the Carleson function of analytic self‐maps of finitely connected domains with smooth boundary are equivalent. Using this result we obtain the characterization of compact composition operators on Hardy–Orlicz spaces.

We give a classification of real hypersurfaces in the complex hyperbolic quadric Q m ∗ = S O 2 , m o / S O 2 S O m that have constant mean curvature and harmonic curvature.

We show that a large collection of special functions, in particular Nielsen's beta function, are generalized Stieltjes functions of order 2, and therefore logarithmically completely monotonic. This includes the Laplace transform of functions of the form x f ( x ) , where f is itself the Laplace transform of a sum of dilations and translations of periodic functions. Our methods are also applied to ratios

We consider rough metrics on smooth manifolds and corresponding Laplacians induced by such metrics. We demonstrate that globally continuous heat kernels exist and are Hölder continuous locally in space and time. This is done via local parabolic Harnack estimates for weak solutions of operators in divergence form with bounded measurable coefficients in weighted Sobolev spaces.

Let S be a split family of del Pezzo surfaces over a discrete valuation ring such that the general fiber is smooth and the special fiber has ADE ‐singularities. Let G be the reductive group given by the root system of these singularities. We construct a G‐torsor over S whose restriction to the generic fiber is the extension of structure group of the universal torsor. This extends a construction of

We prove the existence of good smooth integral models of Shimura varieties of Hodge type in arbitrary unramified mixed characteristic (0, p). As a first application we provide a smooth solution (answer) to a conjecture (question) of Langlands for Shimura varieties of Hodge type. As a second application we prove the existence in arbitrary unramified mixed characteristic (0, p) of integral canonical

In this paper, we define and study Gevrey spaces associated with a Hörmander family of (globally defined) vector fields and its corresponding sub‐Laplacian. We show some natural relations between the various Gevrey spaces in this setting on general manifolds, and more particular properties on Lie groups with polynomial growth of the volume. In the case of the Heisenberg group and of S U ( 2 ) , we

It is a classical result that every C ‐valued holomorphic function has a local power series representation. This even remains true for holomorphic functions with values in a locally complete locally convex Hausdorff space E over C . Motivated by this example we try to answer the following question. Let E be a locally convex Hausdorff space over a field K , let F ( Ω ) be a locally convex Hausdorff

This paper is devoted to the functional analytic approach to the problem of construction of Feller semigroups in the characteristic case via the Fichera function. Probabilistically, our result may be stated as follows: We construct a Feller semigroup corresponding to such a diffusion phenomenon that a Markovian particle moves continuously in the interior of the state space, without reaching the boundary

We consider 3‐dimensional pseudo‐manifolds M ̂ with a given set of marked point V such that M ̂ ∖ V is the interior of a compact 3‐manifold with boundary M. An ideal triangulation T of ( M ̂ , V ) has V as set of vertices. A branching ( T , b ) enhances T to a Δ‐complex. Branched triangulations of ( M ̂ , V ) are considered up to the b‐transit equivalence generated by isotopy and ideal branched moves

For a character χ of a finite group G, the number χ c ( 1 ) = [ G : ker χ ] χ ( 1 ) is called the codegree of χ. Let N be a normal subgroup of G and set Irr ( G | N ) = Irr ( G ) − Irr ( G / N ) . Let p be a prime. In this paper, we first show that if for two distinct prime divisors p and q of | N | , p q divides none of the codegrees of elements of Irr ( G | N ) , then Fit ( N ) ≠ { 1 } and N is either

The generalized fractional integral operators are shown to be bounded from an Orlicz–Hardy space H Φ ( R n ) to another Orlicz–Hardy space H Ψ ( R n ) , where Φ and Ψ are generalized Young functions. The result extends the boundedness of the usual fractional integral operator I α from H p ( R n ) to H q ( R n ) for α , p , q ∈ ( 0 , ∞ ) and − n / p + α = − n / q , which was proved by Stein and Weiss

We prove the existence and uniqueness of μ‐pseudo almost automorphic solution for a delayed non‐autonomous partial functional differential equation in the exponential dichotomic case, where the nonlinear operator F satisfies the φ‐Lipschitz condition and φ belongs to some admissible spaces. We further prove the existence of an invariant stable manifold around the μ‐pseudo almost automorphic solution

This paper is concerned with the following elliptic problem: ( − Δ ) m u = u + m ∗ − 1 + λ u − s 1 φ 1 , in B 1 , u ∈ D 0 m , 2 ( B 1 ) , ( P ) (P)where ( − Δ ) m is the polyharmonic operator, m ∗ = 2 N N − 2 m is the critical Sobolev embedding exponent. B1 is the unit ball in R N , s1 and λ > 0 are parameters, φ 1 > 0 is the eigenfunction of ( − Δ ) m , D 0 m , 2 ( B 1 ) corresponding to the first

For q ≥ 1 we consider the nonlocal ordinary differential equation − a ∫ 0 1 | y | q d s y ′ ′ ( t ) = λ f ( t , y ( t ) ) , 0 < t < 1 , subject to the Dirichlet boundary conditions y ( 0 ) = 0 = y ( 1 ) . Due to the term a ∫ 0 1 | y | q ds appearing in the equation, this is a class of nonlocal differential equations. By using a novel order cone we are able to establish existence of a positive solution

This paper is concerned with well‐posedness of the Cahn–Hilliard equation subject to a class of new dynamic boundary conditions. The system was recently derived in Liu–Wu (Arch. Ration. Mech. Anal. 233 (2019), 167–247) via an energetic variational approach and it naturally fulfils three physical constraints such as mass conservation, energy dissipation and force balance. The target problem examined

We consider weak solutions ( u , π ) : Ω → R n × R to stationary p‐Stokes systems of the type − div a ( x , E u ) + ∇ π + [ D u ] u = f , div u = 0 in Ω ⊂ R n , where the function a ( x , ξ ) satisfies p‐growth conditions in ξ and depends Hölder continuously on x. By E u we denote the symmetric part of the gradient D u and we write [ D u ] u for the convective term. In this setting, we establish results

We prove an extension theorem for ultraholomorphic classes defined by so‐called Braun–Meise–Taylor weight functions ω and transfer the proofs from the single weight sequence case from V. Thilliez to the weight function setting. We are following a different approach than the results obtained in a recent paper by the authors, more precisely we are working with real methods by applying the ultradifferentiable

Following Mumford and Chiodo, we compute the Chern character of the derived pushforward ch ( R • π * O ( D ) ) , for D an arbitrary element of the Picard group of the universal curve over the moduli stack of stable marked curves. This allows us to express the pullback of universal Brill–Noether classes via Abel–Jacobi sections to the compactified universal Jacobians, for all compactifications such

In terms of weak solutions of the fractional p‐Laplace equation with measure data, this paper offers a dual characterization for the fractional Sobolev capacity on bounded domain. In addition, two further results are given: one is an equivalent estimate for the fractional Sobolev capacity; the other is the removability of sets of zero capacity and its relation to solutions of the fractional p‐Laplace

In this paper we look at a probabilistic approach to a non‐local quadratic form that has lately attracted some interest. This form is related to a recently introduced non‐local normal derivative. The goal is to construct two Markov processes: one corresponding to that form and the other which is related to a probabilistic interpretation of the Neumann problem. We also study the Dirichlet‐to‐Neumann

We consider the linearized and nonlinear stationary incompressible flow around rotating and translating body in the exterior domain R 3 ∖ D ¯ , where D ⊂ R 3 is open and bounded, with Lipschitz boundary. We derive the pointwise estimates for the pressure in both cases. Moreover, we consider the linearized problem in a truncation domain D R : = B R ∖ D ¯ of the exterior domain R 3 ∖ D ¯ under certain

The main goal of this paper is to study some properties of an extension of valuations from classical invariants. More specifically, we consider a valued field ( K , ν ) and an extension ω of ν to a finite extension L of K. Then we study when the valuation ring of ω is essentially finitely generated over the valuation ring of ν. We present a necessary condition in terms of classic invariants of the

We study the well‐posedness of the fractional degenerate integro‐differential equations ( P α ) : D α ( M u ) ( t ) = A u ( t ) + ∫ − ∞ t a ( t − s ) A u ( s ) d s + ∫ − ∞ t b ( t − s ) B u ( s ) d s + f ( t ) , ( t ∈ T : = [ 0 , 2 π ] ) , in Lebesgue–Bochner spaces L p ( T ; X ) and Besov spaces B p , q s ( T ; X ) , where A, B and M are closed linear operators on a Banach space X satisfying D ( A

The aim of this paper is to study the existence of solution to an equation involving the Bessel operator in R N ( I − Δ ) α u + λ V ( x ) u = γ f ( x , u ) , where λ , γ are real positive parameters, V : R N → R + is a continuous function, 0 < α < 1 with 2 α < N , f is a continuous function on R N × R which does not satisfy the Ambrosetti–Rabinowitz condition. By using the Fountain theorem and Morse

It is shown that the calculation of the sum of the spaces of the K‐Peetre interpolation method can be reduced to the calculation of the sum of the cones of the concave functions included by the parameter in the definition of the spaces of the K‐Peetre interpolation method. As an example, a new extrapolation theorem for operators in Lipschitz spaces is obtained.

In this manuscript we study geometric regularity estimates for problems driven by fully nonlinear elliptic operators (which can be either degenerate or singular when “the gradient is small”) under strong absorption conditions of the general form: G ( x , D u , D 2 u ) = f ( u ) χ { u > 0 } in Ω , where the mapping u ↦ f ( u ) fails to decrease fast enough at the origin, so allowing that nonnegative

Let G be a regular Lie group which is a directed union of regular Lie groups G i (all modelled on possibly infinite‐dimensional, locally convex spaces). We show that G = lim ⟶ G i as a regular Lie group if G admits a so‐called direct limit chart. Notably, this allows the regular Lie group Diff c ( M ) of compactly supported diffeomorphisms to be interpreted as a direct limit of the regular Lie groups

The goal of this article is to investigate nontrivial m‐quasi‐Einstein manifolds globally conformal to an n‐dimensional Euclidean space. By considering such manifolds, whose conformal factors and potential functions are invariant under the action of an ( n − 1 ) ‐dimensional translation group, we provide a complete classification when λ = 0 and m ≥ 1 or m = 2 − n .

Let M be a Hopf hypersurface in a nonflat complex space form M 2 ( c ) , c ≠ 0 , of complex dimension two. In this paper, we prove that M has η‐recurrent Ricci operator if and only if it is locally congruent to a homogeneous real hypersurface of type (A) or (B) or a non‐homogeneous real hypersurface with vanishing Hopf principal curvature. This is an extension of main results in [17, 21] for real hypersurfaces

In this paper, we consider the scattering theory of the radial solution to focusing energy‐subcritical Hartree equation with inverse‐square potential in the energy space H 1 ( R d ) using the method from [4]. The main difficulties are due to the fact that the equation is not space‐translation invariant and that the nonlinearity is non‐local. Using the radial Sobolev embedding and a virial‐Morawetz

In this article, we study the critical points of the total scalar curvature functional restricted to the space of metrics with constant scalar curvature of unitary volume, for simplicity, CPE metrics. Here, we prove that a CPE metric admitting a non‐trivial closed conformal vector field must be isometric to a round sphere metric, which provides a partial answer to the CPE conjecture.

Homothetic and translating solitons for the inverse mean curvature flow (IMCF) in R n + 1 are self‐similar solutions deformed by only homothety and translation under IMCF, respectively. In this paper, we address some geometric properties of these solitons. To be specific, the incompleteness for the homothetic soliton of velocity C with 0 < C < 1 n and for any translating soliton are proved. In addition

In this paper we present a unified simple approach to anisotropic Hardy inequalities in various settings. We consider Hardy inequalities which involve a Finsler distance from a point or from the boundary of a domain. The sharpness and the non‐attainability of the constants in the inequalities are also proved.

The present paper is concerned with stability of the stationary solution of the Burgers equation in exterior domains in R n . In the previous papers [5, 6, 7] the asymptotic behavior of radially symmetric solutions for the multi‐dimensional Burgers equation in exterior domains in R n , n ≥ 3 , has been considered. The results [5, 6, 7] are restricted to stability of radially solutions within the class

We obtain pointwise upper bounds on the derivatives of the heat kernel on Damek–Ricci spaces and we study the L p ‐boundedness of Littlewood–Paley–Stein operators.

A generically generated vector bundle on a smooth projective variety yields a rational map to a Grassmannian, called Kodaira map. We answer a previous question, raised by the asymptotic behaviour of such maps, giving rise to a birational characterization of abelian varieties. In particular we prove that, under the conjectures of the Minimal Model Program, a smooth projective variety is birational to

We prove a general result about the behaviour of minimizing sequences for nonlocal shape functionals satisfying suitable structural assumptions. Typical examples include functions of the eigenvalues of the fractional Laplacian under homogeneous Dirichlet boundary conditions. Exploiting a nonlocal version of Lions' concentration‐compactness principle, we prove that either an optimal shape exists or

Let Δ and L = Δ − ∥ x ∥ 2 be the Dunkl Laplacian and the Dunkl harmonic oscillator respectively. We define the Hardy space H 1 associated with the Dunkl harmonic oscillator by means of the nontangential maximal function with respect to the semigroup e t L . We prove that the space H 1 admits characterizations by relevant Riesz transforms and atomic decompositions. The atoms which occur in the atomic

We describe the Aluthge transform of an unbounded weighted composition operator acting in an L2‐space. We show that its closure is also a weighted composition operator with the same symbol and a modified weight function. We investigate its dense definiteness. We characterize p‐hyponormality of unbounded weighted composition operators and provide results on how it is affected by the Aluthge transformation

In this paper we prove mixed inequalities for the maximal operator M Φ , for general Young functions Φ with certain additional properties, improving and generalizing some previous estimates for the Hardy–Littlewood maximal operator proved by E. Sawyer. We show that given r ≥ 1 , if u , v r are weights belonging to the A1‐Muckenhoupt class and Φ is a Young function as above, then the inequality u v

This paper introduces both notions of topological entropy and invariance entropy for semigroup actions on general topological spaces. We use the concept of admissible family of open coverings to extending and studying the notions of Adler–Konheim–McAndrew topological entropy, Bowen topological entropy, and invariance entropy to the general theory of topological dynamics.

In this note we study an abstract class of weakly dissipative second‐order systems with finite memory. We establish the polynomial decay of Rivera, Naso and Vegni for the solution of the system under a very weak condition on the relaxation function.

We prove a generalization of the Littlewood–Paley characterisation of the BMO space where the shifts of a Schwartz function are replaced by a family of functions with suitable conditions imposed on them. We also prove that a certain family of Triebel–Lizorkin spaces can be characterized in a similar way.

Let H be a separable Hilbert space with the unit operator I, let A be a bounded linear operator in H with a Schatten–von Neumann Hermitian component ( A − A ∗ ) / 2 i ( A ∗ means the operator adjoint to A) and let f ( z ) be a function analytic on the spectra of A and A ∗ . For f ( A ) we obtain the representation in the form of the sum of a normal operator and a quasi‐nilpotent Schatten–von Neumann

We give an original representation integral formula for the resolvent families associated to the fractional Cauchy equation with memory effects C D t α u ( t ) − A u ( t ) + ∫ 0 t β ( t − s ) A u ( s ) d s = f ( t , u ( t ) ) , t ∈ [ 0 , T ] , T > 0 , where u ( 0 ) = u 0 ∈ X and A is a sectorial operator on a Banach space X. Moreover, we get spatial bounds for the resolvent families in order to study

The study of symmetries is a well known research topic in differential geometry with relevant physical interpretations. Given a Riemannian manifold ( M , g ) , we consider pseudo‐Riemannian g‐natural metrics G on its tangent bundle T M and characterize conformal, homothetic and Killing vector fields of ( T M , G ) obtained from natural lifts of vector fields of M.

Assume that G is a finite group. For every a , b ∈ N , we define a graph Γ a , b ( G ) whose vertices correspond to the elements of G a ∪ G b and in which two tuples ( x 1 , ⋯ , x a ) and ( y 1 , ⋯ , y b ) are adjacent if and only if ⟨ x 1 , ⋯ , x a , y 1 , ⋯ , y b ⟩ = G . We study several properties of these graphs (isolated vertices, loops, connectivity, diameter of the connected components) and

The global existence and asymptotic behavior for anisotropic parabolic equation in R n are considered. By using the classical Galerkin approximation and suitable conditions on the weighted function, it is obtained the global estimate and the uniformly estimates for the global weak solution. Besides, the L 2 ( R n ) ∩ L r ( R n ) global attractor for anisotropic parabolic p‐Laplacian equation is also

Let G be a simple graph on the vertex set [n] and let J G be the corresponding binomial edge ideal. Let G = v ∗ H be the cone of v on H. In this article, we compute all the Betti numbers of J G in terms of the Betti numbers of J H and as a consequence, we get the Betti diagram of wheel graph. Also, we study Cohen–Macaulay defect of S / J G in terms of Cohen–Macaulay defect of S H / J H and using this

For the spaces D L p , L p and M 1 , we consider the topology of uniform convergence on absolutely convex compact subsets of their (pre‐)dual space. Following the notation of J. Horváth's book we call these topologies κ‐topologies. They are given by a neighbourhood basis consisting of polars of absolutely convex and compact subsets of their (pre‐)dual spaces. In many cases it is more convenient to