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arXiv · 2208.06498

Maximal function characterization of Hardy spaces related to Laguerre polynomial expansions

Jorge J. Betancor·Estefanía Dalmasso·Pablo Quijano·Roberto Scotto
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Abstract

In this paper we introduce the atomic Hardy space $\mathcal{H}^1((0,\infty),\gamma_\alpha)$ associated with the non-doubling probability measure $d\gamma_\alpha(x)=\frac{2x^{2\alpha+1}}{\Gamma(\alpha+1)}e^{-x^2}dx$ on $(0,\infty)$, for ${\alpha>-\frac12}$. We obtain characterizations of $\mathcal{H}^1((0,\infty),\gamma_\alpha)$ by using two local maximal functions. We also prove that the truncated maximal function defined through the heat semigroup generated by the Laguerre differential operator is bounded from $\mathcal{H}^1((0,\infty),\gamma_\alpha)$ into $L^1((0,\infty),\gamma_\alpha)$.

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Jorge J. Betancor, Estefanía Dalmasso, Pablo Quijano, Roberto Scotto. 2022-08-12. Maximal function characterization of Hardy spaces related to Laguerre polynomial expansions. https://arxiv.org/abs/2208.06498

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