Matrix Weighted Kolmogorov-Riesz's Compactness Theorem

被引：1

作者：

Liu, Shenyu ^{[1
]}

Yang, Dongyong ^{[1
]}

Zhuo, Ciqiang ^{[2
]}

机构：

[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China

[2] Hunan Normal Univ, Sch Math & Stat, Key Lab Comp & Stochast Math, Minist Educ, Changsha 410081, Peoples R China

来源：

FRONTIERS OF MATHEMATICS | 2023年 / 18卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Kolmogorov-Riesz theorem; matrix weight; totally bounded; metric measure space; variable exponent Lebesgue space; A(P) WEIGHTS; SPACES; SETS;

D O I：

10.1007/s11464-021-0103-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, several versions of the Kolmogorov-Riesz compactness theorem in weighted Lebesgue spaces with matrix weights are obtained. In particular, when the matrix weight W is in the known Ap class, a characterization of totally bounded subsets in Lp(W) with p is an element of (1, infinity) is established.

引用

页码：1167 / 1189

页数：23

共 39 条

[31] Convex body domination and weighted estimates with matrix weights [J].

Nazarov, Fedor ;

Petermichl, Stefanie ;

Treil, Sergei ;

Volberg, Alexander .

ADVANCES IN MATHEMATICS, 2017, 318 :279-306

[32]

Riesz M., 1933, ACTA SCI MATH SZEGED, V6, P136

[33] Matrix-weighted Besov spaces [J].

Roudenko, S .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 355 (01) :273-314

[34] Wavelets and the angle between past and future [J].

Treil, S ;

Volberg, A .

JOURNAL OF FUNCTIONAL ANALYSIS, 1997, 143 (02) :269-308

[35]

Tsuji M., 1952, Kodai Math. Sem. Rep, V3, P33

[36] Matrix A(p) weights via S-functions [J].

Volberg, A .

JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 1997, 10 (02) :445-466

[37]

Willard S., 2004, GeneralTopology

[38] CHARACTERIZATIONS OF WEIGHTED COMPACTNESS OF COMMUTATORS VIA CMO(Rn) [J].

Wu, Huoxiong ;

Yang, Dongyong .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2018, 146 (10) :4239-4254

[39] Weighted Frechet-Kolmogorov Theorem and Compactness of Vector-Valued Multilinear Operators [J].

Xue, Qingying ;

Yabuta, Kozo ;

Yan, Jingquan .

JOURNAL OF GEOMETRIC ANALYSIS, 2021, 31 (10) :9891-9914

← 1 2 3 4 →