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SHARP ESTIMATES FOR FUNCTIONS OF BOUNDED LOWER OSCILLATION

Part of: Harmonic analysis in several variables

Published online by Cambridge University Press:  28 May 2012

ADAM OSȨKOWSKI
ADAM OSȨKOWSKI*
Affiliation:
Department of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland (email: ados@mimuw.edu.pl)
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Abstract

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Let f:ℝ→ℝ be a locally integrable function of bounded lower oscillation. The paper contains the proofs of sharp strong-type, weak-type and exponential estimates for the mean oscillation of f. In particular, this yields the precise value of the norm of the embedding BLO⊂BMOp, 1≤p<∞. Higher-dimensional analogues for anisotropic BLO spaces are also established.

Keywords

BMOBLOBellman functionbest constants

MSC classification

Secondary: 42B37: Harmonic analysis and PDE
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 87 , Issue 1 , February 2013 , pp. 68 - 81
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

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