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arXiv · 2210.14394

Endpoint estimates for harmonic analysis operators associated with Laguerre polynomial expansions

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

In this paper we give a criterion to prove boundedness results for several operators from $H^1((0,\infty),\gamma_\alpha)$ to $L^1((0,\infty),\gamma_\alpha)$ and also from $L^\infty((0,\infty),\gamma_\alpha)$ to $\BMO((0,\infty),\gamma_\alpha)$, with respect to the probability measure $d\gamma_\alpha (x)=\frac{2}{\Gamma(\alpha+1)} x^{2\alpha+1} e^{-x^2} dx$ on $(0,\infty)$ when ${\alpha>-\frac12}$. 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.

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Jorge J. Betancor, Estefanía Dalmasso, Pablo Quijano, Roberto Scotto. 2022-10-26. Endpoint estimates for harmonic analysis operators associated with Laguerre polynomial expansions. https://arxiv.org/abs/2210.14394

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