Weighted norm inequalities for the bilinear maximal operator on variable Lebesgue spaces
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 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 \cite{dcu-f-nPreprint2010} in the variable Lebesgue spaces and the bilinear results of Lerner {\em et al.} \cite{MR2483720} in the classical Lebesgue spaces. As an application we prove weighted norm inequalities for bilinear singular integral operators in the variable Lebesgue spaces.
Keywords
Cite
@article{arxiv.1811.00618,
title = {Weighted norm inequalities for the bilinear maximal operator on variable Lebesgue spaces},
author = {David Cruz-Uribe and Oscar Mauricio Guzman},
journal= {arXiv preprint arXiv:1811.00618},
year = {2019}
}
Comments
Revised based on anonymous referee's reports. A number of typos and small errors corrected. One conjecture added to introduction