Integral operators in Hölder spaces on upper Ahlfors regular sets

Volume and layer potentials are integrals on a subset Y of the Euclidean space Rn that depend on a variable in a subset X of Rn. Here we present a unified approach to some results by assuming that X and Y are subsets of a metric space M and that Y is equipped with a measure ν that satisfies upper Ahlfors growth conditions that include non-doubling measures. We prove continuity statements in the frame of (generalized) Hölder spaces upon variation both of the density functions on Y and of the off-diagonal potential kernel and T1 theorems that generalize corresponding results of J. García-Cuerva and A. E. Gatto in case X = Y for kernels that include the standard ones. © 2023 Accademia Nazionale dei Lincei.