Maximal function characterization of Hardy spaces related to Laguerre polynomial expansions

BETANCOR, JORGE J.; DALMASSO, ESTEFANÍA; QUIJANO, PABLO; SCOTTO, ROBERTO

COLLECTANEA MATHEMATICA

UNIV BARCELONA

Año: 2024

0010-0757

In this paper we introduce the atomic Hardy space $mathcal{H}^1((0,infty),gamma_alpha)$ associated with the non-doubling probability measure $dgamma_alpha(x)=rac{2x^{2alpha+1}}{Gamma(alpha+1)}e^{-x^2}dx$ on $(0,infty)$, for ${alpha>-rac12}$. 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 $L^1((0,infty),gamma_alpha)$.