Description of traces of functions in the Sobolev space with a Muckenhoupt weight

被引：22

作者：

Tyulenev, A. I. ^{[1
]}

机构：

[1] Moscow Inst Phys & Technol, Dolgoprudnyi 141700, Moscow Oblast, Russia

来源：

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS | 2014年 / 284卷 / 01期

基金：

俄罗斯基础研究基金会;

关键词：

Sobolev Space; STEKLOV Institute; Besov Space; Atomic Decomposition; Weighted Sobolev Space;

D O I：

10.1134/S0081543814010209

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We characterize the trace of the Sobolev space W (p) (l) (a"e (n) , gamma) with 1 < p < a and weight gamma a A (p) (loc) (a"e (n) ) on a d-dimensional plane for 1 a parts per thousand currency sign d < n. It turns out that for a function phi to be the trace of a function f a W (p) (l) (a"e (n) , gamma), it is necessary and sufficient that phi belongs to a new Besov space of variable smoothness, , constructed in this paper. The space is compared with some earlier known Besov spaces of variable smoothness.

引用

页码：280 / 295

页数：16

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