Weak type \((1,1)\) estimates of the maximal function for the Laguerre semigroup in finite dimensions
type: Item
instance of: scholarly article
title: Weak type \((1,1)\) estimates of the maximal function for the Laguerre semigroup in finite dimensions
zbMATH Open document ID: 0823.42011
DOI: 10.4171/RMI/118
author: Ulla Dinger
published in: Revista Matemática Iberoamericana
publication date: 1993-01-16T00:00:00Z
full work available at URL: https://eudml.org/doc/39410
review text: Let \(\{T^ t\}_{0< t<\infty}\) be a symmetric diffusion semigroup. The associated maximal operator is defined by \(Mf(x)= \sup_{t> 0} | T^ t f(x)|\). The \(L^ p\), \(p> 1\), boundedness of this operator was proved by E. M. Stein more than twenty years ago. The weak type (1,1) estimate is more delicate and requires some additional properties of the semigroup. In this paper, the weak type (1,1) estimate is proved for the Laguerre semigroup in higher dimensions. Analogous theorems are known for ultraspherical harmonics (B. Muckenhoupt and E. M. Stein), the one- dimensional Laguerre semigroup (B. Muckenhoupt) and the Hermite semigroup in higher dimensions (P. Sjögren).
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 47D03
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 94644
zbMATH Keywords: diffusion semigroup
zbMATH Keywords: maximal operator
zbMATH Keywords: weak type (1,1) estimate
zbMATH Keywords: Laguerre semigroup
reviewed by: Do Ngoc Diep
MaRDI profile type: Publication
OpenAlex ID: W2048781376
description: scientific article; zbMATH DE number 94644