# Multidimensional Paley-Zygmund theorems and sharp $L^p$ estimates for some elliptic operators

Abstract : The goal of the paper is twofold. Firstly we study sufficient conditions of convergence for random series of eigenfunctions in $L^\infty$. The eigenfunctions are considered with respect to a reference elliptic operator like the Laplace-Beltrami operator or a Schrödinger operator with growing potential on the Euclidean space. That is a generalization of an old result due to Paley and Zygmund. Secondly, we obtain a few optimal $L^p$ bounds of eigenfunctions including a generalization of the Bernstein inequality. We show that the previous two themes are intimately linked.
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Preprints, Working Papers, ...

Cited literature [14 references]

https://hal.archives-ouvertes.fr/hal-01572331
Contributor : Rafik Imekraz <>
Submitted on : Sunday, August 6, 2017 - 10:02:14 PM
Last modification on : Thursday, January 11, 2018 - 6:21:23 AM

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• HAL Id : hal-01572331, version 1

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Rafik Imekraz. Multidimensional Paley-Zygmund theorems and sharp $L^p$ estimates for some elliptic operators. 2017. ⟨hal-01572331⟩

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