Extrapolation and weighted norm inequalities in the variable Lebesgue spaces

2014/08/19 by Cruz-Uribe, David, Wang, Li-An Daniel · 3 citations
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1408.4499

Abstract

We extend the theory of Rubio de Francia extrapolation, including off-diagonal, limited range, and A_∞ extrapolation, to the weighted variable Lebesgue spaces. As a consequence we are able to show that a number of different operators from harmonic analysis are bounded on these spaces. The proofs of our extrapolation results are developed in a way that outlines a general approach to proving extrapolation theorems on other Banach function spaces.

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• Extrapolation for bilinear compact operators in the variable exponent setting
• Recent results on matrix weighted norm inequalities
• Characterization of Vanishing Campanato Spaces via Ball Banach Function Spaces and Its Applications

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