Pointwise Conditions for Membership of Functions in Weighted Sobolev Classes

IF 0.6 4区数学 Q3 MATHEMATICS

Functional Analysis and Its Applications Pub Date : 2022-10-10 DOI:10.1134/S0016266322020022

V. I. Bogachev

引用次数: 0

Abstract

According to a known characterization, a function \(f\) belongs to the Sobolev space \(W^{p,1}(\mathbb{R}^n)\) of functions contained in \(L^p(\mathbb{R}^n)\) along with their generalized first-order derivatives precisely when there is a function \(g\in L^p(\mathbb{R}^n)\) such that

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加权Sobolev类中函数隶属性的点态条件

根据已知的表征，一个函数\(f\)属于包含在\(L^p(\mathbb{R}^n)\)中的函数及其广义一阶导数的Sobolev空间\(W^{p,1}(\mathbb{R}^n)\)，精确地当存在一个函数\(g\in L^p(\mathbb{R}^n)\)使得

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来源期刊

Functional Analysis and Its Applications 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Functional Analysis and Its Applications publishes current problems of functional analysis, including representation theory, theory of abstract and functional spaces, theory of operators, spectral theory, theory of operator equations, and the theory of normed rings. The journal also covers the most important applications of functional analysis in mathematics, mechanics, and theoretical physics.