# Discrete Hardy spaces and heat semigroup associated with the discrete Laplacian

24 Oct 2018 Almeida Víctor Betancor Jorge J. Mesa Lourdes Rodríguez

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 $\ell^p(\mathbb Z)$, $0<p\leq 1$... (read more)

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