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arXiv · 1810.10415

Discrete Hardy spaces and heat semigroup associated with the discrete Laplacian

Víctor Almeida·Jorge J. Betancor·Lourdes Rodríguez Mesa
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Abstract

In this paper we study the behavior of some harmonic analysis operators associated with the discrete Laplacian $\Delta_d$ in discrete Hardy spaces $\mathcal H^p(\mathbb Z)$. We prove that the maximal operator and the Littlewood-Paley $g$ function defined by the semigroup generated by $\Delta_d$ are bounded from $\mathcal H^p(\mathbb Z)$ into $\ell^p(\mathbb Z)$, $0<p\leq 1$. Also, we establish that every $\Delta_d$-spectral multiplier of Laplace transform type is a bounded operator from $\mathcal H^p(\mathbb Z)$ into itself, for every $0<p\leq 1$.

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Víctor Almeida, Jorge J. Betancor, Lourdes Rodríguez Mesa. 2018-10-24. Discrete Hardy spaces and heat semigroup associated with the discrete Laplacian. https://arxiv.org/abs/1810.10415

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