Discrete Hölder spaces and their characterization via semigroups associated with the discrete Laplacian and kernel estimates

Abstract In this paper, we characterize the discrete Hölder spaces by means of heat and Poisson semigroups associated with Laplacian. These characterizations allow us to get regularity properties fractional powers Laplacian Bessel potentials along these also in Zygmund a more direct way than using pointwise definition spaces. To obtain our results, it has been crucial boundedness kernels their derivatives both space time variables. We believe that estimates are independent interest.