This article is cited in 4 papers

Classes of kernels and continuity properties of the tangential gradient of an integral operator in Hölder spaces on a manifold

M. Lanza de Cristoforis

Dipartimento di Matematica ‘Tullio Levi-Civita’, Università degli Studi di Padova, Via Trieste 63, Padova I-35121,Italy

Abstract: We prove multiplication and embedding theorems for classes of kernels of integral operators in subsets of metric spaces with a measure. Then we prove a tangential differentiation theorem with respect to a semi-tangent vector for integral operators that are defined on an upper-Ahlfors regular subset of the Euclidean space and a continuity theorem for the corresponding integral operator in Hölder spaces in the specific case of a differentiable manifold.

Keywords and phrases: continuity, classes of kernels, tangential gradient, integral operator, manifold.

MSC: Primary 31B10; Secondary 42B20, 42B37, 47G40, 47G10

Received: 15.08.2022

Language: English

DOI: 10.32523/2077-9879-2023-14-3-54-74