Resumen de Maximal function characterization of Hardy spaces related to Laguerre polynomial expansions

Jorge Juan Betancor Pérez , Estefanía Dalmasso, Pablo Quijano, R. Scotto

• 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 >-\frac{1}{2}}. 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 ).