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arXiv · 2305.03656

A necessary condition on a singular kernel for the continuity of an integral operator in H\"{o}lder spaces

Massimo Lanza de Cristoforis
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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.

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Massimo Lanza de Cristoforis. 2023-05-05. A necessary condition on a singular kernel for the continuity of an integral operator in H\"{o}lder spaces. https://arxiv.org/abs/2305.03656

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