Boundedness of Journe operators with matrix weights

被引：9

作者：

Domelevo, K. ^{[1
]}

Kakaroumpas, S. ^{[1
]}

Petermichl, S. ^{[1
]}

Soler i Gibert, O. ^{[1
]}

机构：

[1] Julius Maximilians Univ Wurzburg, Campus Hubland Nord,Emil Fischer Str 40, D-97074 Wurzburg, Germany

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2024年 / 532卷 / 02期

基金：

欧洲研究理事会;

关键词：

Journe operators; Matrix weights; Biparameter weighted estimates; Sparse domination; SINGULAR-INTEGRALS; A(P) WEIGHTS; SPACES; REPRESENTATION; INEQUALITIES; BMO;

D O I：

10.1016/j.jmaa.2023.127956

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We develop a biparameter theory for matrix weights and provide various biparameter matrix-weighted bounds for Journe operators as well as other central operators under the assumption of the product matrix Muckenhoupt condition. In particular, we provide a complete theory for biparameter Journe operator bounds on matrix -weighted L2 spaces. We also achieve bounds in the general case of matrix-weighted Lp spaces, for 1 < p < infinity for parapro duct-free Journe operators. Finally, we expose an open problem involving a matrix-weighted Fefferman-Stein inequality, on which our methods rely in the general setting of matrix-weighted bounds for arbitrary Journe operators and p not equal 2. (c) 2023 Elsevier Inc. All rights reserved.

引用

页数：66

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