Hölder regularity of the solutions of Fredholm integral equations on upper Ahlfors regular sets

2025/10/09 by Lanza_de_Cristoforis, M., Norman, M.
#31B10 #45B05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2510.08264

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.

Citations

• A survey on the boundary behavior of the double layer potential in Schauder spaces in the frame of an abstract approach
• Birth and life of the L² boundedness of the Cauchy Integral on Lipschitz graphs
• Boundedness on inhomogeneous Lipschitz spaces of fractional integrals, singular integrals and hypersingular integrals associated to non-doubling measures
• Boundedness properties of fractional integral operators associated to non--doubling measures
• Lipschitz spaces and Calderon-Zygmund operators associated to non-doubling measures

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