Weighted inequalities for product fractional integrals
Abstract
We investigate one and two weight norm inequalities for product fractional integrals. We show that in the one weight case, most of the 1 parameter theory carries over to the 2 parameter setting. However, in the two weight case, apart from the trivial case of product weights, the rectangle characteristic never controls the operator norm without side conditions. The Stein-Weiss extension of the classical Hardy-Littlewood-Sobolev inequality carries over to the setting of 2 parameters with nonproduct power weights using a sandwiching technique.
Keywords
Cite
@article{arxiv.1702.03870,
title = {Weighted inequalities for product fractional integrals},
author = {Eric T. Sawyer and Zipeng Wang},
journal= {arXiv preprint arXiv:1702.03870},
year = {2018}
}
Comments
56 pages. We thank Hitoshi Tanaka for pointing out an error in our counterexample involving rectangle A1 weights. An error also occurred in our counterexample involving the two-tailed characteristic. The remaining counterexamples and positive results are unchanged