Strong type inequalities and an almost-orthogonality principle for families of maximal operators along directions in R2

被引：14

作者：

Alfonseca, A ^{[1
]}

机构：

[1] Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain

来源：

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES | 2003年 / 67卷

关键词：

D O I：

10.1112/S0024610702003915

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The paper proves an almost-orthogonality principle for maximal operators over arbitrary sets of directions in IR2. Namely, the L-p-bounds for an operator of this type are obtained from the corresponding L-p-bounds of the maximal functions associated to a certain partition of the set of directions, and from the particular structure of this partition. Applications to several types of maximal operators are provided.

引用

页码：208 / 218

页数：11

共 5 条

[1] A remark on maximal operators along directions in R2
Alfonseca, A
Soria, F
Vargas, A
MATHEMATICAL RESEARCH LETTERS, 2003, 10 (01) : 41 - 49
[2] An almost-orthogonality principle in L2 for directional maximal functions
Alfonseca, A
Soria, F
Vargas, A
HARMONIC ANALYSIS AT MOUNT HOLYOKE, 2003, 320 : 1 - 7
[3] A Unified Version of Weighted Weak Type Inequalities for One-Sided Maximal Function on R2
Zhang, Erxin
Ren, Yanbo
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2023, 46 (04)
[4] Weighted inequalities for Fourier multiplier operators of Bochner–Riesz type on R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathbb{R} ^2$$\end{document}
S. Sato
Acta Mathematica Hungarica, 2023, 171 (2) : 301 - 324
[5] A Unified Version of Weighted Weak Type Inequalities for One-Sided Maximal Function on R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}^2$$\end{document}
Erxin Zhang
Yanbo Ren
Bulletin of the Malaysian Mathematical Sciences Society, 2023, 46 (4)

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