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On maximal functions and parabolic limits

✍ Scribed by Jan Chabrowski

Publisher: Springer-Verlag
Year: 1983
Tongue: French
Weight: 406 KB
Volume: 184
Category: Article
ISSN: 0025-5874
DOI: 10.1007/bf01252862

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## Abstract Let __A~t~f__(__x__) denote the mean of __f__ over a sphere of radius __t__ and center __x__. We prove sharp estimates for the maximal function __M~E~ f__(__X__) = sup~t~∈~__E__~ |A__tf__(x)| where __E__ is a fixed set in IR^+^ and __f__ is a radial function ∈ __L__^__p__^(IR^__d__^). L