The $H^p(\mathbb{Z}^n)-H^q(\mathbb{Z}^n)$ boundedness of the discrete Riesz potential

Pablo Rocha

The $H^p(\mathbb{Z}^n)-H^q(\mathbb{Z}^n)$ boundedness of the discrete Riesz potential

Pablo Rocha

Abstract

In [J. Class. Anal., vol. 26 (1) (2025), 63-76], we proved that the discrete Riesz potential $I_α$ is a bounded operator $H^p(\mathbb{Z}^n) \to H^q(\mathbb{Z}^n)$ for $\frac{n-1}{n} < p \leq 1$, $\frac{1}{q} = \frac{1}{p} - \fracα{n}$ and $0 < α< n$. In this note, we extend such boundedness on the full range $0 < p \leq 1$.

The $H^p(\mathbb{Z}^n)-H^q(\mathbb{Z}^n)$ boundedness of the discrete Riesz potential

Abstract

In [J. Class. Anal., vol. 26 (1) (2025), 63-76], we proved that the discrete Riesz potential

is a bounded operator

for

and

. In this note, we extend such boundedness on the full range

The $H^p(\mathbb{Z}^n)-H^q(\mathbb{Z}^n)$ boundedness of the discrete Riesz potential

Abstract

The $H^p(\mathbb{Z}^n)-H^q(\mathbb{Z}^n)$ boundedness of the discrete Riesz potential

Abstract

Paper Structure

Table of Contents

Theorems & Definitions (4)