August 18, 2024Open Access

A molecular decomposition for Hᵖ (Zⁿ) and applications

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Abstract

In this work, for the range n-1n < p 1, we give a molecular reconstruction theorem for Hᵖ (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_ defined on Zⁿ is a bounded operator Hᵖ (Zⁿ) Hq (Zⁿ) for n-1n < p < n and 1q = 1p - n, where 0 < < n.

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Pablo Rocha (Sun,) studied this question.

synapsesocial.com/papers/68e5bd48b6db643587555972 https://doi.org/https://doi.org/10.48550/arxiv.2408.09528

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