Endpoint mapping properties of spherical maximal operators

Details Endpoint mapping properties of spherical maximal operators Endpoint mapping properties of spherical maximal operators

2002-05-14

arxiv.org/abs/math/0205153v1

Journal de l'Institut Math\'ematiques de Jussieu, 2 (2003), 109-144.

Mathematics

Classical Analysis and ODEs

28 pages

Scientific paper

For a function $f\in L^p(\Bbb R^d)$, $d\ge 2$, let $A_t f(x)$ be the mean of
$f$ over the sphere of radius $t$ centered at $x$. Given a set $E\subset
(0,\infty)$ of dilations we prove endpoint bounds for the maximal operator
$M_E$ defined by $M_E f(x)=\sup_{t\in E} |A_t f(x)|$.

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