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April 16, 2026Mathematical Methods in the Applied Sciences0 citationsOpen Access

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

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MCMassimo Lanza de CristoforisMNManuel 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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Cite This Study

Cristoforis et al. (2026) studied this question.

synapsesocial.com/papers/69e07d732f7e8953b7cbe534https://doi.org/10.1002/mma.70725
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