On Hardy-Littlewood and Fefferman-Stein strong maximal functions
type: Item
instance of: scholarly article
title: On Hardy-Littlewood and Fefferman-Stein strong maximal functions
zbMATH Open document ID: 0904.42014
DOI: 10.1007/BF02320377
published in: Mathematical Notes
publication date: 1998-12-29T00:00:00Z
review text: The estimate \[ (M_s f)^*(t)\leq c(f^\#_s)^*(t/2)+f^*(2t) \] is proved, where \(M_s f\) and \(f^\#_s\) are the Hardy-Littlewood and the Fefferman-Stein strong maximal functions, respectively, and \((.)^*\) denotes nonincreasing permutation. Similar estimate for usual maximal functions implies the Fefferman-Stein theorem [see \textit{R. A. DeVore} and \textit{R. C. Sharpley}, Mem. Am. Math. Soc. 293, 115 p. (1984; Zbl 0529.42005)].
Mathematics Subject Classification ID: 42B25
zbMATH DE Number: 1158917
zbMATH Keywords: strong Hardy-Littlewood maximal function
zbMATH Keywords: strong Fefferman-Stein maximal function
zbMATH Keywords: nonincreasing permutation
zbMATH Keywords: mean oscillation
zbMATH Keywords: Fefferman-Stein theorem
author: Andrei K. Lerner
reviewed by: Maria Roginskaya
MaRDI profile type: Publication
cites work: \(H^p\) spaces of several variables
cites work: Q3254471
cites work: Q4039801
cites work: Weak-\(L^\infty\) and BMO
cites work: Maximal functions measuring smoothness
cites work: A geometric proof of the strong maximal theorem
full work available at URL: https://doi.org/10.1007/bf02320377
OpenAlex ID: W2049914451
description: scientific article; zbMATH DE number 1158917