A necessary condition on a singular kernel for the continuity of an integral operator in H\"{o}lder spaces
Functional Analysis
2023-05-08 v1
Abstract
We prove that a condition of boundedness of the maximal function of a singular integral operator, that is known to be sufficient for the continuity of the corresponding integral operator in H\"{o}lder spaces, is actually also necessary in case the action of the integral operator does not decrease the regularity of a function. We do so in the frame of metric measured spaces with a measure satisfying certain growth conditions that include nondoubling measures. Then we present an application to the case of an integral operator defined on a compact differentiable manifold.
Keywords
Cite
@article{arxiv.2305.03656,
title = {A necessary condition on a singular kernel for the continuity of an integral operator in H\"{o}lder spaces},
author = {Massimo Lanza de Cristoforis},
journal= {arXiv preprint arXiv:2305.03656},
year = {2023}
}