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.
Funding agency
Grant number
GNAMPA-INdAM
CUP_E53C22001930001
The author acknowledges the support of the Research Project GNAMPA-INdAM CUP_E53C22001930001 ‘Operatori differenziali e integrali in geometria spettrale’.
Citation:
M. Lanza de Cristoforis, “Classes of kernels and continuity properties of the tangential gradient of an integral operator in Hölder spaces on a manifold”, Eurasian Math. J., 14:3 (2023), 54–74
\Bibitem{Lan23}
\by M.~Lanza de Cristoforis
\paper Classes of kernels and continuity properties of the tangential gradient of an integral operator in H\"older spaces on a manifold
\jour Eurasian Math. J.
\yr 2023
\vol 14
\issue 3
\pages 54--74
\mathnet{http://mi.mathnet.ru/emj477}
\crossref{https://doi.org/10.32523/2077-9879-2023-14-3-54-74}
Linking options:
https://www.mathnet.ru/eng/emj477
https://www.mathnet.ru/eng/emj/v14/i3/p54
This publication is cited in the following 1 articles:
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