Wavelet Characterization of Local Muckenhoupt Weighted Sobolev Spaces with Variable Exponents

被引：3

作者：

Izuki, Mitsuo ^{[1
]}

Nogayama, Toru ^{[2
]}

Noi, Takahiro ^{[2
]}

Sawano, Yoshihiro ^{[3
,4
]}

机构：

[1] Tokyo City Univ, Fac Liberal Arts & Sci, Setagaya Ku, 1-28-1 Tamadutsumi, Tokyo 1588557, Japan

[2] Tokyo Metropolitan Univ, Dept Math Sci, Hachioji, Tokyo 1920397, Japan

[3] Chuo Univ, Dept Math Sci, Bunkyo Ku, Kasuga, Tokyo 1128551, Japan

[4] Peoples Friendship Univ Russia, Moscow, Russia

来源：

CONSTRUCTIVE APPROXIMATION | 2023年 / 57卷 / 01期

基金：

日本学术振兴会;

关键词：

Variable exponent; Wavelet; Sobolev spaces; Local Muckenhoupt weight; LEBESGUE SPACES; MODULAR INEQUALITIES; MAXIMAL OPERATOR; DECOMPOSITIONS; AMALGAMS; BESOV; LP;

D O I：

10.1007/s00365-022-09573-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The goal of this paper is to define local weighted variable Sobolev spaces of fractional and negative order and their characterization by wavelets. We first consider local weighted variable Sobolev spaces by means of weak derivatives and obtain a wavelet characterization for these spaces. Using the Bessel potentials, we next define local weighted variable Sobolev spaces of fractional order. We show that Sobolev spaces obtained by weak derivatives and those by the Bessel potentials coincide. Finally, using duality, we define local weighted variable Sobolev spaces with negative order. We also show that local weighted variable Sobolev spaces are closed under complex interpolation. Some examples are given including the applications to weighted uniformly local Lebesgue spaces with variable exponents and periodic function spaces as a by-product, although the exponent is constant.

引用

页码：161 / 234

页数：74