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
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
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