Speaker：Jorge J. Betancor（Universidad de la Laguna，Spain）

Time：2023-02-13, 16:50-18:10

Location：Zoom APP：（1）16：50-17：30 please log in：880 6113 3940（Pwd：C9sn28）  （2）17：30-18：10 please log in：879 4514 5198（Pwd：xr8Fn6）

Abstract:

In this talk we will discuss boundedness properties of harmonic analysis operators (Maximal operators defined by semigroups, Riesz transforms, Littlewood-Paley functions, multipliers and variation operators) associated with $\alpha$-Laguerre polynomial expansions. Firstly, we consider variable Lebesgue spaces $L^p(.)(0,\infty)^n, d\gamma_\alpha)$, where $d\gamma_\alpha(x)=\prod_{j=1}^n\frac{x_j^{\alpha_j} e^{-x_j}}{\Gamma(\alpha_j+1)}$ and $\alpha=(\alpha_1, \ldots, \alpha_n) \in(0, \infty)^n$. In the second part we study the Hardy space $H^1((0, \infty), \gamma_\alpha)$. This Hardy space is characterized by using local maximal functions. The dual of $H^1(0, \infty), \gamma_\alpha)$ is a BMO-type space. We discuss some endpoint estimates $(p=1$ and $p=\infty)$ for Laguerre harmonic analysis operators.