Two weight Sobolev norm inequalities for fractional vector Riesz transforms and doubling weights
Classical Analysis and ODEs
2024-04-05 v2
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 A_2 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.
Cite
@article{arxiv.2207.14684,
title = {Two weight Sobolev norm inequalities for fractional vector Riesz transforms and doubling weights},
author = {Eric T. Sawyer and Brett D. Wick},
journal= {arXiv preprint arXiv:2207.14684},
year = {2024}
}
Comments
An error was found in the treatment of the stopping form in the previous version, and as a result, the T1 theorem is weakened - it applies only to fractional vector Riesz transforms now. The other main theorems remain unchanged