๐”– Bobbio Scriptorium
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Directional operators and radial functions on the plane

โœ Scribed by Javier Duoandikoetxea; Ana Vargas

Book ID
112781381
Publisher
Springer Netherlands
Year
1995
Tongue
English
Weight
453 KB
Volume
33
Category
Article
ISSN
0004-2080

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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~โˆˆ~__E__~ |A__tf__(x)| where __E__ is a fixed set in IR^+^ and __f__ is a radial function โˆˆ __L__^__p__^(IR^__d__^). L