Discrete H\"older spaces, their characterization via semigroups associated to the discrete Laplacian and kernels estimates
Classical Analysis and ODEs
2021-07-15 v1 Analysis of PDEs
Functional Analysis
Abstract
In this paper we characterize the discrete H\"older spaces by means of the heat and Poisson semigroups associated to the discrete Laplacian. These characterizations allow us to get regularity properties of fractional powers of the discrete Laplacian and the Bessel potentials along these spaces and also in the discrete Zygmund spaces in a more direct way than using the pointwise definition of the spaces. To obtain our results, it has been crucial to get boundedness properties of the heat and Poisson kernels and their derivatives in both space and time variables. We believe that these estimates are also of independent interest.
Keywords
Cite
@article{arxiv.2107.06778,
title = {Discrete H\"older spaces, their characterization via semigroups associated to the discrete Laplacian and kernels estimates},
author = {Luciano Abadias and Marta De León-Contreras},
journal= {arXiv preprint arXiv:2107.06778},
year = {2021}
}