Energy conditions and twisted localizations of operators
Classical Analysis and ODEs
2018-01-16 v2
Abstract
We show that the energy conditions are not necessary for boundedness of fractional Riesz transforms in dimension at least 2. We also give a weak converse, namely that the energy conditions are necessary for boundedness of families of twisted localizations of fractional singular integrals having the positive gradient property.
Keywords
Cite
@article{arxiv.1801.03706,
title = {Energy conditions and twisted localizations of operators},
author = {Eric T. Sawyer},
journal= {arXiv preprint arXiv:1801.03706},
year = {2018}
}
Comments
32 pages. The kernels of the localized operators satisfy only one-sided CZ smoothness estimates, correcting a mistake in the first version. The main result on failure of necessity of energy for Riesz transforms is unaffected