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Linear and nonlinear Bessel potentials associated with the Poly-axially operator
Integral Transforms and Special Functions ( IF 0.7 ) Pub Date : 2020-09-27 , DOI: 10.1080/10652469.2020.1825413
Belgacem Selmi 1 , Chahiba Khelifi 1
Affiliation  

ABSTRACT

In this work, we will study a Bessel potential spaces Wαs,p(R+n), (sR,1p<+,α=(α1,,αn)Rn,α1>12,,αn>12) associated with the Poly-axially operator Δα and their properties. We define the Sobolev type spaces Eαm,p(R+n)(mN,0N,1p<+) and we prove an analogue of Calderón's theorem for Fourier-Bessel transform. We define the nonlinear Bessel potentials associated with a measure ν and the Lαp-capacity. Finally, we establish a classical problem of existence of an extremal function for the Lαp-capacity.



中文翻译:

与多轴算子相关的线性和非线性贝塞尔势

摘要

在这项工作中,我们将研究贝塞尔潜在空间 w ^αsp[R+ñ,(s[R1个p<+α=α1个αñ[Rñα1个>-1个2个αñ>-1个2个)与多轴运算符相关联 Δα及其属性。我们定义Sobolev类型空间Eαp[R+ññ0ñ1个p<+),我们证明了傅立叶-贝塞尔变换的卡尔德隆定理的类似物。我们定义了与测度ν相关的非线性贝塞尔电位和大号αp-容量。最后,我们建立了一个极值函数存在的经典问题。大号αp-容量。

更新日期:2020-09-27
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