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Best Constants for Uncentred Maximal Functions
Author(s) -
Grafakos Loukas,
MontgomerySmith Stephen
Publication year - 1997
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609396002081
Subject(s) - mathematics , maximal function , maximal operator , norm (philosophy) , operator (biology) , operator norm , function (biology) , pure mathematics , combinatorics , mathematical analysis , operator theory , biochemistry , chemistry , repressor , evolutionary biology , biology , political science , transcription factor , law , bounded function , gene
We precisely evaluate the operator norm of the uncentred Hardy–Littlewood maximal function on L p (R 1 ). Consequently, we compute the operator norm of the ‘strong’ maximal function on L p (R n ), and we observe that the operator norm of the uncentred Hardy–Littlewood maximal function over balls on L p (R n ) grows exponentially as n →∞. 1991 Mathematics Subject Classification 42B25.