The H^p(ℤⁿ)-H^q(ℤⁿ) boundedness of the discrete Riesz potential

2025/08/28 by Pablo Rocha, Rocha, Pablo
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2508.20342

openalex publication_date 2025/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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(ℤⁿ) → H^q(ℤⁿ) for (n-1)/(n) < p ≤ 1, (1)/(q) = (1)/(p) - \fracαn and 0 < α< n. In this note, we extend such boundedness on the full range 0 < p ≤ 1.

Citations

• Fractional series operators on discrete Hardy spaces
• Duality in spaces of finite linear combinations of atoms
• Hp spaces of several variables

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• A molecular decomposition for H^p(ℤⁿ)
• Estimates for Riesz potential on weighted variable Hardy spaces revisited
• Boundedness of generalized Riesz potentials on the variable Hardy spaces
• Classical discrete operators on variable ℓ^p(⋅)(ℤ) spaces