A molecular decomposition for H^p(ℤⁿ)

2024/08/18 by Pablo Rocha, Rocha, Pablo
Computer Science · Mathematics · #Advanced Algebra and Geometry #Classical Analysis and ODEs (math.CA) #Cryptography and Residue Arithmetic #FOS: Mathematics #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.2408.09528

openalex publication_date 2024/08/18 · openalex created_date 2024/09/21 · openalex updated_date 2026/07/28

Abstract

In this work, for the range (n-1)/(n) < p ≤ 1, we give a molecular reconstruction theorem for H^p(ℤⁿ). As an application of this result and the atomic decomposition developed by S. Boza and M. Carro in [Proc. R. Soc. Edinb., 132 A (1) (2002), 25-43], we prove that the discrete Riesz potential I_α defined on ℤⁿ is a bounded operator H^p(ℤⁿ) → H^q(ℤⁿ) for (n-1)/(n) < p < \fracnα and (1)/(q) = (1)/(p) - \fracαn, where 0 < α< n.

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