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arXiv · 2501.18342

Regularity properties of certain convolution operators in H\"{o}lder spaces

Matteo Dalla Riva·Massimo Lanza de Cristoforis·Paolo Musolino
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Abstract

The aim of this paper is to prove a theorem of C.~Miranda on the H\"older regularity of convolution operators acting on the boundary of an open set in the limiting case in which the open set is of class $C^{1,1}$ and the densities are of class $C^{0,1}$. The convolution operators that we consider are generalizations of those that are associated to layer potential operators, which are a useful tool for the analysis of boundary value problems.

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Matteo Dalla Riva, Massimo Lanza de Cristoforis, Paolo Musolino. 2025-01-30. Regularity properties of certain convolution operators in H\"{o}lder spaces. https://arxiv.org/abs/2501.18342

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