Endpoint estimates for harmonic analysis operators associated with Laguerre polynomial expansions

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

MATHEMATISCHE NACHRICHTEN

WILEY-V C H VERLAG GMBH

Año: 2024

0025-584X

In this paper we give a criterion to prove boundedness results for several operators from $H^1((0,\infty)^d,\gamma_\alpha)$ to $L^1((0,\infty)^d,\gamma_\alpha)$ and also from $L^\infty((0,\infty)^d,\gamma_\alpha)$ to $\textup{BMO}((0,\infty)^d,\gamma_\alpha)$, with respect to the probability measure $d\gamma_\alpha (x)=\prod_{j=1}^d\frac{2}{\Gamma(\alpha_j+1)} x_j^{2\alpha_j+1} e^{-x_j^2} dx_j$ on $(0,\infty)^d$ when $\alpha=(\alpha_1, \dots,\alpha_d)$ is a multi-index in $\left(-\frac12,\infty\right)^d$. We shall apply it to establish endpoint estimates for Riesz transforms, maximal operators, Littlewood-Paley functions, multipliers of Laplace transform type, fractional integrals and variation operators in the Laguerre setting.