Two weight Sobolev norm inequalities for fractional vector Riesz transforms and doubling weights

2022/07/29 by Sawyer, Eric T., Wick, Brett D.
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA

paper · doi:10.48550/arxiv.2207.14684

Abstract

We prove a T1 theorem for fractional vector Riesz transforms mapping one weighted Sobolev space to another, where the weights are doubling measures on Euclidean space. Boundedness is characterized by the classical A₂ condition and two dual testing conditions on indicators of cubes. We also show the equivalence of various weighted Sobolev norms when the measure is doubling, something that fails in general.

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