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

2018/11/01 by Cruz-Uribe, David, Guzman, Oscar Mauricio · 2 citations
#42B25 #42B35 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1811.00618

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 \citedcu-f-nPreprint2010 in the variable Lebesgue spaces and the bilinear results of Lerner \em et al. \citeMR2483720 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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• Extrapolation for bilinear compact operators in the variable exponent setting
• Recent results on matrix weighted norm inequalities

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