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 H\"{o}lder spaces in the specific case of a differentiable manifold.
CLASSES OF KERNELS AND CONTINUITY PROPERTIES OF THE TANGENTIAL GRADIENT OF AN INTEGRAL OPERATOR IN HÖLDER SPACES ON A MANIFOLD
Lanza de Cristoforis, M.
Writing – Original Draft Preparation
2023
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 H\"{o}lder spaces in the specific case of a differentiable manifold.
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