SHARP LOCAL LOWER L p -BOUNDS FOR DYADIC-LIKE MAXIMAL OPERATORS

SHARP LOCAL LOWER L p -BOUNDS FOR DYADIC-LIKE MAXIMAL OPERATORS

We provide sharp lower L p -bounds for the localized dyadic maximal operator on ℝ n when the local L 1 and the local L p norm of the function are given. We actually do that in the more general context of homogeneous trees in probability spaces. For this we use an effective linearization for such max...

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Veröffentlicht in:Proceedings of the American Mathematical Society 2013-09, Vol.141 (9), p.3171-3181
Hauptverfasser: MELAS, ANTONIOS D., NIKOLIDAKIS, ELEFTHERIOS, STAVROPOULOS, THEODOROS
Format: Artikel
Sprache:eng
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Zusammenfassung:We provide sharp lower L p -bounds for the localized dyadic maximal operator on ℝ n when the local L 1 and the local L p norm of the function are given. We actually do that in the more general context of homogeneous trees in probability spaces. For this we use an effective linearization for such maximal operators on an adequate set of functions.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-2013-11789-2