Endpoint mapping properties of spherical maximal operators

Andreas Seeger; Terence Tao; James Wright

doi:10.1017/S1474748003000057

Endpoint mapping properties of spherical maximal operators

Andreas Seeger, Terence Tao, James Wright

Research output: Contribution to journal › Article › peer-review

25 Citations (Scopus)

Abstract

For a function [formula omitted], [formula omitted], let [formula omitted] be the mean of [formula omitted] over the sphere of radius [formula omitted] centred at [formula omitted]. Given a set [formula omitted] of dilations we prove various endpoint bounds for the maximal operator [formula omitted] defined by [formula omitted], under some regularity assumptions on [formula omitted].

Original language	English
Pages (from-to)	109-144
Number of pages	36
Journal	Journal of the Institute of Mathematics of Jussieu
Volume	2
Issue number	1
DOIs	https://doi.org/10.1017/S1474748003000057
Publication status	Published - Jan 2003
Externally published	Yes

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title = "Endpoint mapping properties of spherical maximal operators",

abstract = "For a function [formula omitted], [formula omitted], let [formula omitted] be the mean of [formula omitted] over the sphere of radius [formula omitted] centred at [formula omitted]. Given a set [formula omitted] of dilations we prove various endpoint bounds for the maximal operator [formula omitted] defined by [formula omitted], under some regularity assumptions on [formula omitted].",

keywords = "maximal operators, spherical means",

author = "Andreas Seeger and Terence Tao and James Wright",

year = "2003",

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doi = "10.1017/S1474748003000057",

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T1 - Endpoint mapping properties of spherical maximal operators

AU - Seeger, Andreas

AU - Tao, Terence

AU - Wright, James

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N2 - For a function [formula omitted], [formula omitted], let [formula omitted] be the mean of [formula omitted] over the sphere of radius [formula omitted] centred at [formula omitted]. Given a set [formula omitted] of dilations we prove various endpoint bounds for the maximal operator [formula omitted] defined by [formula omitted], under some regularity assumptions on [formula omitted].

AB - For a function [formula omitted], [formula omitted], let [formula omitted] be the mean of [formula omitted] over the sphere of radius [formula omitted] centred at [formula omitted]. Given a set [formula omitted] of dilations we prove various endpoint bounds for the maximal operator [formula omitted] defined by [formula omitted], under some regularity assumptions on [formula omitted].

KW - maximal operators

KW - spherical means

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U2 - 10.1017/S1474748003000057

DO - 10.1017/S1474748003000057

M3 - Article

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EP - 144

JO - Journal of the Institute of Mathematics of Jussieu

JF - Journal of the Institute of Mathematics of Jussieu

IS - 1

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Endpoint mapping properties of spherical maximal operators

Abstract

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