End-point maximal regularity for the discrete parabolic Cauchy problem and regularity of non-local operators in discrete Besov spaces

In this paper we prove both end-point maximal L1-regularity for the discrete parabolic Cauchy problem and regularity of some non-local operators in discrete Besov spaces. To that aim, we prove characterizations of the discrete Besov spaces in terms of the heat and Poisson semigroups associated with...

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Bibliographic Details
Authors: Abadías, Luciano, León-Contreras, Marta de, Mahillo Cazorla, Alejandro|||0000-0003-4189-0268
Format: article
Publication Date:2025
Country:España
Institution:Universidad de Cantabria (UC)
Repository:UCrea Repositorio Abierto de la Universidad de Cantabria
Language:English
OAI Identifier:oai:dnet:ucreareposit::53288bf8bfc8f2792dbc4ed664099a79
Online Access:https://hdl.handle.net/10902/39747
Access Level:Open access
Keyword:Maximal L1-regularity
Discrete Besov spaces
Discrete heat and Poisson semigroups
Regularity of discrete fractional operators
Description
Summary:In this paper we prove both end-point maximal L1-regularity for the discrete parabolic Cauchy problem and regularity of some non-local operators in discrete Besov spaces. To that aim, we prove characterizations of the discrete Besov spaces in terms of the heat and Poisson semigroups associated with the discrete Laplacian. Moreover, we provide new estimates for the derivatives of the discrete heat kernel and semigroup which are of independent interest.

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