Regularity of averages over hypersurfaces
type: Item
instance of: scholarly article
title: Regularity of averages over hypersurfaces
zbMATH Open document ID: 0722.42008
DOI: 10.1007/BF02386371
author: Lennart Börjeson
published in: Arkiv för Matematik
publication date: 1989-01-01T00:00:00Z
review text: The author studies averages over smooth measures on smooth compact hypersurfaces in \({\mathbb{R}}^ n\). His results are closely related to the recent works of \textit{L. Colzani} [J. Aust. Math. Soc., Ser. A 41, 287-297 (1986; Zbl 0616.43010)], \textit{M. Cowling} and \textit{G. Mauceri} [Trans. Am. Math. Soc. 296, 341-365 (1986; Zbl 0651.42007)] and \textit{J. L. Rubio de Francia} [Duke Math. J. 53, 395-404 (1986; Zbl 0612.42008)]. If some assumptions are made on the decay of the Fourier transform of the measure defining the averages, then mixed norm estimates for these means can be obtained. As a consequence, \(L^ p\) estimates of multiparameter maximal functions are obtained.
Mathematics Subject Classification ID: 42B25
zbMATH DE Number: 4190387
zbMATH Keywords: averages
zbMATH Keywords: smooth compact hypersurfaces
zbMATH Keywords: multiparameter maximal functions
reviewed by: D. C. Struppa
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02386371
OpenAlex ID: W2062283544
description: scientific article; zbMATH DE number 4190387