The paper [10] raised the question of what the possible Hilbert functions are for fat point subschemes of the form 2p 1+...+2p r, for all possible choices ofr distinct points in ℙ2. We study this problem forr points in ℙ2 over an algebraically closed fieldk of arbitrary characteristic in case eitherr ≤ 8 or the points lie on a (possibly reducible) conic. In either case, it follows from [17, 18] that

A weighted theory for multilinear fractional integral operators and maximal functions is presented. Sufficient conditions for the two weight inequalities of these operators are found, including “power and logarithmic bumps” and anA ∞ condition. For one weight inequalities a necessary and sufficient condition is then obtained as a consequence of the two weight inequalities. As an application, Poincaré

We obtainL p estimates for parametric Marcinkiewicz integrals associated to polynomial mappings and with rough kernels on the unit sphere as well as on the radial direction. These estimates will allow us to use an extrapolation argument to obtain some new and improved results on Marcinkiewicz integrals. Also, such estimates provide us with a unifying approach in dealing with Marcinkiewicz integrals

In this paper, written for non specialists, we discuss several points in the elementary theory of almost complex manifolds, with a focus on the question of choice of special coordinates and on the obstruction given by the Nijenhuis tensor.

We consider differences of weighted composition operators between given weighted Bergman spaces Hν ∞ of infinite order and characterize boundedness and the essential norm of these differences.

We show that Ahypergeometric systems and Horn hypergeometric systems are Weyl closed for very generic parameters.

Several transformation and summation formulae for nonterminating basic hypergeometric series are established through the modified Abel lemma on summation by parts.

We give equivalent conditions for tensor product of Orlicz sequence spaces, then we obtain a necessary and sufficient condition for a class of matrix operators acting on Orlicz sequence spaces to be continuous and compact.

The notion of ball proximinality and the strong ball proximinality were recently introduced in [2]. We prove that an equable subspaceY of a Banach spaceX is strongly ball proximinal and the metric projection fromX, onto the closed unit ball ofY, is Hausdorff metric continuous.

Letρ C be the regularity of the Hilbert function of a projective curveC inP n K over an algebraically closed fieldK andβ 1,...,β n-1 be degrees for which there exists a complete intersection of type (β 1,...,β n-1) containing properlyC. Then the Castelnuovo-Mumford regularity ofC is bounded above by max {ρ C + 1,β 1 +...+β n-1-(n-1)}. We investigate the sharpness of the above bound, which is achieved

Hesse claimed in [7] (and later also in [8]) that an irreducible projective hypersurface in ℙn defined by an equation with vanishing hessian determinant is necessarily a cone. Gordan and Noether proved in [6] that this is true forn≤3 and constructed counterexamples for everyn≥4. Gordan and Noether and Franchetta gave classification of hypersurfaces in ℙ4 with vanishing hessian and which are not cones

Hilbert schemes of zerodimensional ideals in a polynomial ring can be covered with suitable affine open subschemeswhose construction is achieved using border bases. Moreover, border bases have proved to be an excellent tool for describing zero-dimensional ideals when the coefficients are inexact. and in this situation they show a clear advantage with respect to Gröbner bases which, nevertheless, can

In the context of a finite measure metric space whose measure satisfies a growth condition, we prove “T1” type necessary and sufficient conditions for the boundedness of fractional integrals, singular integrals, and hypersingular integrals on inhomogeneous Lipschitz spaces. We also indicate how the results can be extended to the case of infinite measure. Finally we show applications to Real and Complex

The spaceT d;n ofn tropically collinear points in a fixed tropical projective space\(\mathbb{T}\mathbb{P}^{d - 1} \) is equivalent to the tropicalization of the determinantal variety of matrices of rank at most 2, which consists of reald×n matrices of tropical or Kapranov rank at most 2, modulo projective equivalence of columns. We show that it is equal to the image of the moduli space\(\mathcal{M}_{0

Let (R;m) be a local ring of Krull dimensiond andI ⊆R be an ideal with analytic spreadd. We show that thej-multiplicity ofI is determined by the Rees valuations ofI centered on m. We also discuss a multiplicity that is the limsup of a sequence of lengths that grow at anO(n d) rate.

In this paper some numerical restrictions for surfaces with an involution are obtained. These formulas are used to study surfaces of general typeS withp g =q = 1 having an involutioni such thatS/i is a nonruled surface and such that the bicanonical map ofS is not composed withi. A complete list of possibilities is given and several new examples are constructed, as bidouble covers of surfaces. In particular

Let\(\mathcal{L} \equiv - \Delta + V\) be the Schrödinger operator in ℝn, whereV is a nonnegative function satisfying the reverse Hölder inequality. Let ρ be an admissible function modeled on the known auxiliary function determined byV. In this paper, the authors establish several characterizations of the space BMOρ(ℝn) in terms of commutators of several different localized operators associated to

The construction of families of Sato Grassmannians, their determinant line bundles and the extensions induced by them are given. The base scheme is an arbitrary scheme.

We establish theorems on the existence and asymptotic characterization of solutions of a differential equation of neutral type with deviated argument on neutral type. The mentioned differential equation admits both delayed and advanced arguments. In our considerations we use technique linking measures of noncompactness with the Tikhonov fixed point principle in suitable Frechet space. This approach

We introduce and study the space curves of “h-extremal type”, that are curves of degreed and arithmetic genusg whose Rao function agrees, in a suitable interval depending ond andh, with the one of the “h-extremal” curves introduced by NotariSabadini. Our study is motivated by the literature of the last years concerning curves with large cohomology and their relations with the Hilbert scheme. p] Our

We characterize boundedness and compactness of Volterra composition operators acting between weighted Bergman spacesA v,p and weighted Bloch type spacesB w .

We prove some weighted refinements of the classical Strichartz inequalities for initial data in the Sobolev spaces Ḣs(ℝn). We control the weightedL 2-norm of the solution of the free Schrödinger equation whenever the weight is in a Morrey-Campanato type space adapted to that equation. Our partial positive results are complemented by some necessary conditions based on estimates for certain particular

We provide two alternative proofs of the following formulation of Stein’s lemma obtained by Sagher and Zhou [6]: there exists a constant A > 0 such that for any measurable setE⊂ [0, 1], |E| ≠ 0, there is an integerN that depends only onE such that for any square-summable real-valued sequence {ck} =0/∞ k we have: $$A \cdot \sum\limits_{k > N} {\left| {c_k } \right|} ^2 \leqslant \mathop {sup}\limits_I

The aim is to study the boundary controllability of a system modelling the vibrations of a network ofN Euler-Bernoulli beams serially connected by (N − 1) vibrating interior point masses. Using the classical Hilbert Uniqueness Method, the control problem is reduced to the obtention of an observability inequality. The solution is then expressed in terms of Fourier series so that one of the sufficient

It is shown that for 1 < p1, p2 < 1, 1/p3 = 1/p1 + 1/p2, p3 ≥ 1 there existsC 1 (independent ofn) such that $$\left\| {R_k (f,g)} \right\|_{L^{p_3 } (\mathbb{R}^n )} \leqslant C_1 \left\| f \right\|_{L^{p_1 } (\mathbb{R}^n )} \left\| g \right\|_{L^{p_2 } (\mathbb{R}^n )} $$ where $$R_k (f, g)(x) = b_n \mathop {\lim }\limits_{\varepsilon \to 0} \int_{\left| y \right| > \varepsilon } { f} (x - y)g(x

LetF be an infinite field and letn,p 1,p 2,p 3 be positive integers such thatn =p 1 +p 2 +p 3. Let\(C_{1,2} \in F^{p_1 \times p_2 } \),\(C_{1,3} \in F^{p_1 \times p_3 } \) and\(C_{2,1} \in F^{p_2 \times p_1 } \). In this paper we show that appart from an exception, there always exist\(C_{1,1} \in F^{p_1 \times p_1 } \),\(C_{2,2} \in F^{p_2 \times p_2 } \) and\(C_{2,3} \in F^{p_2 \times p_3 } \) such

We correct an inaccuracy in [1].

LetS be the group ℝd ⋉ ℝ+ endowed with the Riemannian symmetric space metricd and the right Haar measure ρ The space (S, d, ρ) is a Lie group of exponential growth. In this paper we define an Hardy spaceH 1 and aBMO space in this context. We prove that the functions inBMO satisfy the John-Nirenberg inequality and thatBMO may be identified with the dual space ofH 1. We then prove that singular integral

We focus on the rational cohomology of Cornalba’s moduli space of spin curves of genus 1 withn marked points. In particular, we show that both its first and its third cohomology group vanish and the second cohomology group is generated by boundary classes.

We prove an exact, i.e., formulated without Δ-expansions, Ramsey principle for infinite block sequences in vector spaces over countable fields, where the two sides of the dichotomic principle are represented by respectively winning strategies in Gowers’ block sequence game and winning strategies in the infinite asymptotic game. This allows us to recover Gowers’ dichotomy theorem for block sequences

The dominant rational maps of finite degree from a fixed variety to varieties of general type, up to birational isomorphisms, form a finite set. This has been known as the Iitaka-Severi conjecture, and is nowdays an established result, in virtue of some recent advances in the theory of pluricanonical maps. We study the question of finding some effective estimate for the finite number of maps, and to

The article studies the geometry of curves onK3 surfaces. Its aim is to give an alternative proof to the fact that there are rational curves on every projectiveK3 surface.

Let (Ω, Σ, μ) be a σ-finite measure space and let\(\mathcal{L}(X,Y)\) stand for the space of all bounded linear operators between Banach spaces (X; ‖ • ‖ X ) and (Y; ‖ • ‖ Y ). We study the problem of integral representation of linear operators from an Orlicz-Bochner spaceL ϕ(μ,X) toY with respect to operator measures\(m : \sum \to \mathcal{L}(X,Y) \). It is shown that a linear operatorT:L ϕ (μ,X)

In this paper, we obtain a new characterization of Hilbert spaces by means of polynomial mappings, extending the linear result of Kwapień.

For a locally convex space with the topology given by a family {p(┬; α)} α ∈ ω of seminorms, we study the existence and uniqueness of fixed points for a mapping defined on some set. We require that there exists a linear and positive operatorK, acting on functions defined on the index set Ω, such that for everyu, Under some additional assumptions, one of which is the existence of a fixed point for the

We construct an orthonormal basis for the family of bi-variate α-modulation spaces. The construction is based on local trigonometric bases, and the basis elements are closely related to so-called brushlets. As an application, we show thatm-term nonlinear approximation with the representing system in an α-modulation space can be completely characterized.

The purpose of this paper is to prove a new topological fact about the Poincaré and related groups. IfG is a group, say that G is an algebraically determined Polish (i.e., complete separable metric topological) group if, wheneverH is a Polish group and ϕ:H → G is an algebraic isomorphism, then ϕ is a topological isomorphism. The proper Lorentz group, the proper orthochronous Lorentz group and the Heisenberg

LetR be a prime ring of characteristic different from 2,U the Utumi quotient ring ofR, C the extended centroid ofR, F andG non-zero generalized derivations ofR andf(x 1, ...,x n ) a polynomial overC. Denote byf(R) the set {f(r1, ..., rn): r1, ..., rn ∃ R} of all the evaluations off(x 1, ...,x n ) inR. Suppose thatf(x 1, ...,x n ) is not central valued onR. IfR does not embed inM 2(K), the algebra of

We prove that transplantations for Jacobi polynomials can be derived from representation of a special integral operator as fractionalWeyl’s integral. Furthermore, we show that, in a sense, Jacobi transplantation can be reduced to transplantations for ultraspherical polynomials. As an application of these results, we obtain transplantation theorems for Jacobi polynomials in ReH 1 and BMO. The paper

Let 1

Given a functionb, and using adapted Haar wavelets, we define a BMO-type norm which is dependent onb. In both global and local cases, we find the dependence of the bounds on ∥f∥BMO by the bounds on theb-weighted BMO norm off. We show that the dependence is sharp in the global case. Multiscale analysis is used in the local case. We formulate as corollaries global and local dyadicT(b) theorems whose

Let (Ω, Σ) be a measurable space andm: Σ →X be a vector measure with values in the complex Banach space X: We apply the Calderón interpolation methods to the family of spaces of scalarp-integrable functions with respect tom with 1≤p≤∞. Moreover we obtain a result about the relation between the complex interpolation spaces [X 0,X 1][θ] and [X0,X 1][θ] for a Banach couple of interpolation (X 0,X 1) such

In the paper we obtain a characterization of an inequality for Riemann-Liouville operator involving suprema in case of nonincreasing weights.

We consider two independent Gaussian processes that admit a representation in terms of a stochastic integral of a deterministic kernel with respect to a standard Wiener process. In this paper we construct two families of processes, from a unique Poisson process, the finite dimensional distributions of which converge in law towards the finite dimensional distributions of the two independent Gaussian

Let I be an ideal of a commutative Noetherian ring R. It is shown that the R-modules \(H^i_I(M)\) are I-cofinite, for all finitely generated R-modules M and all \(i\in {\mathbb {N}}_0\), if and only if the R-modules \(H^i_I(R)\) are I-cofinite with dimension not exceeding 1, for all integers \(i\ge 2\); in addition, under these equivalent conditions it is shown that, for each minimal prime ideal \({{\mathfrak

We use techniques from time-frequency analysis to show that the space \({\mathcal{S}}_\omega\) of rapidly decreasing \(\omega\)-ultradifferentiable functions is nuclear for every weight function \(\omega (t)=o(t)\) as t tends to infinity. Moreover, we prove that, for a sequence \((M_p)_p\) satisfying the classical condition (M1) of Komatsu, the space of Beurling type \({\mathcal{S}}_{(M_p)}\) when

The Orlicz spaces \(X^{\varPhi }\) associated to a quasi-Banach function space X are defined by replacing the role of the space \(L^1\) by X in the classical construction of Orlicz spaces. Given a vector measure m, we can apply this construction to the spaces \(L^1_w(m),\)\(L^1(m)\) and \(L^1(\Vert m\Vert )\) of integrable functions (in the weak, strong and Choquet sense, respectively) in order to

A gauge\(\gamma\) in a vector space X is a distance function given by the Minkowski functional associated to a convex body K containing the origin in its interior. Thus, the outcoming concept of gauge spaces\((X, \gamma )\) extends that of finite dimensional real Banach spaces by simply neglecting the symmetry axiom (a viewpoint that Minkowski already had in mind). If the dimension of X is even, then

We give an explicit formula for the Hilbert–Poincaré series of the parity binomial edge ideal of a complete graph \(K_{n}\) or equivalently for the ideal generated by all \(2\times 2\)-permanents of a \(2\times n\)-matrix. It follows that the depth and Castelnuovo–Mumford regularity of these ideals are independent of n.

Hironaka’s characteristic polyhedron is an important combinatorial object reflecting the local nature of a singularity. We prove that it can be determined without passing to the completion if the local ring is a G-ring and if additionally either it is Henselian, or a certain polynomiality condition (Pol) holds, or a mild condition (*) on the singularity holds. For example, the latter is fulfilled if

In this paper we prove the conjectured upper bound for Castelnuovo–Mumford regularity of binomial edge ideals posed in [23], in the case of chordal graphs. Indeed, we show that the regularity of any chordal graph G is bounded above by the number of maximal cliques of G, denoted by c(G). Moreover, we classify all chordal graphs G for which \(\mathcal {L}(G)=c(G)\), where \(\mathcal {L}(G)\) is the sum

Suppose that M is a finitely-generated graded module (generated in degree 0) of codimension \(c\ge 3\) over a polynomial ring and that the regularity of M is at most \(2a-2\) where \(a\ge 2\) is the minimal degree of a first syzygy of M. Then we show that the sum of the betti numbers of M is at least \(\beta _0(M)(2^c + 2^{c-1})\). Additionally, under the same hypothesis on the regularity, we establish

Let G be a connected and finite graph with the set of vertices V and the set of edges E. Let \(M_{G}\) be the Hardy–Littlewood maximal function defined on graph G and \(M_{\upalpha ,G}\)\((0\le \upalpha <1)\) be its fractional version. In this paper, the regularity problems related to \(M_{G}\) and \(M_{\upalpha ,G}\) will be studied. We show that \(M_{G}:\mathrm{BV}_p (G)\rightarrow \mathrm{BV}_p(G)\)

In this paper, the \(L^2 \times L^{\infty } \rightarrow L^2\) and \(L^2 \times L^2 \rightarrow L^1\) estimates of bilinear Fourier multiplier operators are discussed under weak smoothness conditions on multipliers. As an application, we prove the \(L^2 \times BMO \rightarrow L^2\) and \(L^2 \times L^2 \rightarrow H^1\) boundedness of bilinear operators with multipliers of limited smoothness satisfying

We give two-weighted norm estimates for higher order commutator of classical operators such as singular integral and fractional type operators, between weighted \(L^p\) and certain spaces that include Lipschitz, BMO and Morrey spaces. We also give the optimal parameters involved with these results, where the optimality is understood in the sense that the parameters defining the corresponding spaces

The objective of this work is an existence proof for variational solutions u to parabolic minimizing problems. Here, the functions being considered are defined on a metric measure space \(({\mathcal {X}}, d, \mu )\). For such parabolic minimizers that coincide with Cauchy-Dirichlet data \(\eta \) on the parabolic boundary of a space-time-cylinder \(\varOmega \times (0, T)\) with an open subset \(\varOmega

We study the nuclearity of the Gelfand–Shilov spaces \({\mathcal {S}}^{({\mathfrak {M}})}_{({\mathscr {W}})}\) and \({\mathcal {S}}^{\{{\mathfrak {M}}\}}_{\{{\mathscr {W}}\}}\), defined via a weight (multi-)sequence system \({\mathfrak {M}}\) and a weight function system \({\mathscr {W}}\). We obtain characterizations of nuclearity for these function spaces that are counterparts of those for Köthe

We consider the dynamics of transcendental self-maps of the punctured plane, \(\mathbb {C}^*=\mathbb {C}{\setminus } \{0\}\). We prove that the escaping set \(I(f)\) is either connected, or has infinitely many components. We also show that \(I(f)\cup \{0,\infty \}\) is either connected, or has exactly two components, one containing 0 and the other \(\infty \). This gives a trichotomy regarding the

We give an algebraic and self-contained proof of the existence of the so-called Noetherian operators for primary submodules over general classes of Noetherian commutative rings. The existence of Noetherian operators accounts to provide an equivalent description of primary submodules in terms of differential operators. As a consequence, we introduce a new notion of differential powers which coincides

For a monomial ideal I, we consider the ith homological shift ideal of I, denoted by \({\text {HS}}_i(I)\), that is, the ideal generated by the ith multigraded shifts of I. Some algebraic properties of this ideal are studied. It is shown that for any monomial ideal I and any monomial prime ideal P, \({\text {HS}}_i(I(P))\subseteq {\text {HS}}_i(I)(P)\) for all i, where I(P) is the monomial localization