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arXiv · 1811.00618

Weighted norm inequalities for the bilinear maximal operator on variable Lebesgue spaces

David Cruz-Uribe·Oscar Mauricio Guzman
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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 $\A_\pp$ 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.

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David Cruz-Uribe, Oscar Mauricio Guzman. 2018-11-01. Weighted norm inequalities for the bilinear maximal operator on variable Lebesgue spaces. https://arxiv.org/abs/1811.00618

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