Translator Disclaimer
2019 Hardy-Littlewood Maximal Operator on the Associate Space of a Banach Function Space
Alexei Yu. Karlovich
Real Anal. Exchange 44(1): 119-140 (2019). DOI: 10.14321/realanalexch.44.1.0119

Abstract

Let \(\mathcal{E}(X,d,\mu)\) be a Banach function space over a space of homogeneous type \((X,d,\mu)\). We show that if the Hardy-Littlewood maximal operator \(M\) is bounded on the space \(\mathcal{E}(X,d,\mu)\), then its boundedness on the associate space \(\mathcal{E}'(X,d,\mu)\) is equivalent to a certain condition \(\mathcal{A}_\infty\). This result extends a theorem by Andrei Lerner from the Euclidean setting of \(\mathbb{R}^n\) to the setting of spaces of homogeneous type.

Citation

Download Citation

Alexei Yu. Karlovich. "Hardy-Littlewood Maximal Operator on the Associate Space of a Banach Function Space." Real Anal. Exchange 44 (1) 119 - 140, 2019. https://doi.org/10.14321/realanalexch.44.1.0119

Information

Published: 2019
First available in Project Euclid: 27 June 2019

zbMATH: 07088967
MathSciNet: MR3951338
Digital Object Identifier: 10.14321/realanalexch.44.1.0119

Subjects:
Primary: 43A85, 46E30.

Rights: Copyright © 2019 Michigan State University Press

JOURNAL ARTICLE
22 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.44 • No. 1 • 2019
Back to Top