What question did this study set out to answer?

The aim is to establish Hölder continuity results for solutions to Fredholm integral equations in metric measured spaces.

April 16, 2026Open Access

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Hölder Regularity of the Solutions of Fredholm Integral Equations on Upper Ahlfors Regular Sets

MCMassimo Lanza de CristoforisUniversity of Padua MNManuel Norman

Key Points

The aim is to establish Hölder continuity results for solutions to Fredholm integral equations in metric measured spaces.
Extended analysis to metric measured spaces with upper Ahlfors growth conditions.
Examined solutions of Fredholm integral equations of the second kind.
Considered cases with nondoubling measures.
Validated Hölder continuity results for solutions under specific growth conditions.
Demonstrated applicability to a wider class of measures.

Abstract

ABSTRACT We extend to the context of metric measured spaces, with a measure that satisfies upper Ahlfors growth conditions, the validity of (generalized) Hölder continuity results for the solution of a Fredholm integral equation of the second kind. Here we note that upper Ahlfors growth conditions include also cases of nondoubling measures.

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Hölder Regularity of the Solutions of Fredholm Integral Equations on Upper Ahlfors Regular Sets

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