The Hp(Zn)-Hq(Zn) boundedness of the discrete Riesz potential

In [J. Class. Anal. 26 (2025), 63–76], we proved that the discrete Riesz potential Iα is a bounded operator Hp(Zn)→Hq(Zn) for n−1n<p≤1, 1q=1p−αn and 0<α<n. In this note, we extend this result to the full range 0<p≤1.

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Publication Details

Journal
Bulletin of the Polish Academy of Sciences Mathematics
Published
2025-09-19
DOI
https://doi.org/10.4064/ba250821-29-8
Primary Topic
Quantum Mechanics and Non-Hermitian Physics
Type
article
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article

The Hp(Zn)-Hq(Zn) boundedness of the discrete Riesz potential

Pablo Rocha
Bulletin of the Polish Academy of Sciences Mathematics
Quantum Mechanics and Non-Hermitian Physics
article

The Hp(Zn)-Hq(Zn) boundedness of the discrete Riesz potential

Pablo Rocha
article en

Abstract

In [J. Class. Anal. 26 (2025), 63–76], we proved that the discrete Riesz potential Iα is a bounded operator Hp(Zn)→Hq(Zn) for n−1n<p≤1, 1q=1p−αn and 0<α<n. In this note, we extend this result to the full range 0<p≤1.

Bulletin of the Polish Academy of Sciences Mathematics
Instituto de Física del Sur (AR), Universidad Nacional del Sur (AR)
Openalex Percentile: Top 80%
Quantum Mechanics and Non-Hermitian Physics
DOIOpen Access PDFOpenAlex
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The Hp(Zn)-Hq(Zn) boundedness of the discrete Riesz potential — Pablo Rocha · Bulletin of the Polish Academy of Sciences Mathematics (2025) | TGRS Research Map | TGRS