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A note about the discrete Riesz potential on $\mathbb{Z}^n$

Pablo Rocha

Abstract

In this note we prove that the discrete Riesz potential $I_α$ defined on $\mathbb{Z}^n$ is a bounded operator $H^p (\mathbb{Z}^n) \to \ell^q (\mathbb{Z}^n)$ for $0 < p \leq 1$ and $\frac{1}{q} = \frac{1}{p} - \fracα{n}$, where $0 < α< n$.

A note about the discrete Riesz potential on $\mathbb{Z}^n$

Abstract

In this note we prove that the discrete Riesz potential defined on is a bounded operator for and , where .
Paper Structure (3 sections, 47 equations)

This paper contains 3 sections, 47 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. The $H^p(\mathbb{Z}^n) - \ell^q(\mathbb{Z}^n)$ boundedness of $I_{\alpha}$

Theorems & Definitions (4)

  • proof
  • proof
  • proof
  • proof