The Two Weight Inequality for Hilbert Transform, Coronas, and Energy Conditions
Classical Analysis and ODEs
2011-08-12 v1
Abstract
We consider the two weight problem for the Hilbert transform, namely the question of finding real-variable characterization of those pair of weights for which the Hilbert transform acts boundedly on of the weights. Such a characterization is known subject to certain side conditions. We give a new proof, simpler in many details, of the best such result. In addition, we analyze underlying assumptions in the proof, especially in terms of two alternate side conditions. A new characterization in the case of one doubling weight is given.
Cite
@article{arxiv.1108.2319,
title = {The Two Weight Inequality for Hilbert Transform, Coronas, and Energy Conditions},
author = {Michael T. Lacey and Eric T. Sawyer and Chun-Yen Shen and Ignacio Uriarte-Tuero},
journal= {arXiv preprint arXiv:1108.2319},
year = {2011}
}
Comments
24 pages, 1 figure