Regularity properties of certain convolution operators in Hölder spaces

Abstract

The aim of this paper is to prove a theorem of C.~Miranda on the Hölder 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.

arXiv admin note: text overlap with arXiv:2409.11132, arXiv:2408.17192