Translator Disclaimer
2020 Weighted norm inequalities for the bilinear maximal operator on variable Lebesgue spaces
D. Cruz-Uribe OFS, O. M. Guzmán
Publ. Mat. 64(2): 453-498 (2020). DOI: 10.5565/PUBLMAT6422004

Abstract

We extend the theory of weighted norm inequalities on variable Lebesgue spaces to the case of bilinear operators. We introduce a bilinear version of the variable $\mathcal{A}_{p(\cdot)}$ condition and show that it is necessary and sufficient for the bilinear maximal operator to satisfy a weighted norm inequality. Our work generalizes the linear results of the first author, Fiorenza, and Neugebauer [7] in the variable Lebesgue spaces and the bilinear results of Lerner et al. [22] in the classical Lebesgue spaces. As an application we prove weighted norm inequalities for bilinear singular integral operators in the variable Lebesgue spaces.

Citation

Download Citation

D. Cruz-Uribe OFS. O. M. Guzmán. "Weighted norm inequalities for the bilinear maximal operator on variable Lebesgue spaces." Publ. Mat. 64 (2) 453 - 498, 2020. https://doi.org/10.5565/PUBLMAT6422004

Information

Received: 2 November 2018; Revised: 30 September 2019; Published: 2020
First available in Project Euclid: 3 July 2020

zbMATH: 07236050
MathSciNet: MR4119260
Digital Object Identifier: 10.5565/PUBLMAT6422004

Subjects:
Primary: 42B25 , 42B35

Keywords: bilinear maximal operator , variable Lebesgue spaces , weights‎

Rights: Copyright © 2020 Universitat Autònoma de Barcelona, Departament de Matemàtiques

JOURNAL ARTICLE
46 PAGES

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

SHARE
Vol.64 • No. 2 • 2020
Back to Top