Discrete Hölder spaces, their characterization via semigroups associated to the discrete Laplacian and kernels estimates

2021/07/14 by Luciano Abadías, Abadias, Luciano, Marta De León-Contreras +1
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2107.06778

openalex publication_date 2021/07/14 · openalex created_date 2021/07/19 · openalex updated_date 2026/07/28

Abstract

In this paper we characterize the discrete Hölder 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.

Citations

• Regularity properties of Schrödinger operators
• Regularity of the obstacle problem for a fractional power of the laplace operator

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