Pseudo-differential operators on ${\mathbb{Z}}^n$ with applications to discrete fractional integral operators

Abstract

In this manuscript we provide necessary and sufficient conditions for the $\text{weak}(1,p)$ boundedness, $1<p<\infty ,$ of discrete Fourier multipliers (Fourier multipliers on ${\mathbb{Z}}^n$). Our main goal is to apply the results obtained to discrete fractional integral operators. Discrete versions of the Calderón-Vaillancourt Theorem and the Gohberg Lemma also are proved.

14 pages

References in corpus (3)

• The essential spectrum of Schrödinger operators on lattices
• On the endpoint regularity of discrete maximal operators
• Essential spectra and exponential estimates of eigenfunctions of lattice operators of quantum mechanics