REMARK ON MEDIAN OSCILLATION DECOMPOSITION AND DYADIC POINT WISE DOMINATION

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http://hdl.handle.net/10138/307061

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Hanninen , T S 2017 , ' REMARK ON MEDIAN OSCILLATION DECOMPOSITION AND DYADIC POINT WISE DOMINATION ' , Houston Journal of Mathematics , vol. 43 , no. 1 , pp. 183-197 .

Title: REMARK ON MEDIAN OSCILLATION DECOMPOSITION AND DYADIC POINT WISE DOMINATION
Author: Hanninen, Timo S.
Contributor organization: Department of Mathematics and Statistics
Date: 2017
Language: eng
Number of pages: 15
Belongs to series: Houston Journal of Mathematics
ISSN: 0362-1588
URI: http://hdl.handle.net/10138/307061
Abstract: In this note, we extend Lerner's local median oscillation decomposition to arbitrary (possibly non-doubling) measures. In the light of the analogy between median and mean oscillation, our extension can be viewed as a median oscillation decomposition adapted to the dyadic (martingale) BMO. As an application of the decomposition, we give an alternative proof for the dyadic (martingale) John-Nirenberg inequality, and for Lacey's domination theorem, which states that each martingale transform is pointwise dominated by a positive dyadic operator of zero complexity. Furthermore, by using Lacey's recent technique, we give an alternative proof for Conde-Alonso and Rey's domination theorem, which states that each positive dyadic operator of arbitrary complexity is pointwise dominated by a positive dyadic operator of zero complexity.
Subject: Median oscillation decomposition
dyadic pointwise domination
non-doubling measures
CALDERON-ZYGMUND OPERATORS
DOUBLING MEASURES
THEOREM
SPACES
111 Mathematics
Peer reviewed: Yes
Usage restriction: restrictedAccess
Self-archived version: submittedVersion


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