Geodesic
Classes of kernels and continuity properties of the tangential gradient of an integral operator in H\"older spaces on a manifold
Eurasian mathematical journal, Tome 14 (2023) no. 3, pp. 54-74

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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. 
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     author = {M. Lanza de Cristoforis},
     title = {Classes of kernels and continuity properties of the tangential gradient of an integral operator in {H\"older} spaces on a manifold},
     journal = {Eurasian mathematical journal},
     pages = {54--74},
     publisher = {mathdoc},
     volume = {14},
     number = {3},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2023_14_3_a3/}
}
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M. Lanza de Cristoforis. Classes of kernels and continuity properties of the tangential gradient of an integral operator in H\"older spaces on a manifold. Eurasian mathematical journal, Tome 14 (2023) no. 3, pp. 54-74. http://geodesic.mathdoc.fr/item/EMJ_2023_14_3_a3/