Positive operators and maximal operators in a filtered measure space

2012/04/30 by Hitoshi Tanaka, Tanaka, Hitoshi, Yutaka Terasawa +1
Mathematics · #42B25 #60G46 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Probability (math.PR) #math.CA #math.PR #msc:42B25 #msc:60G46

paper · pdf · doi:10.48550/arxiv.1204.6600

23 pages; v2:Typos corrected, v3:Typos corrected, references added. To appear in Journal of Functional Analysis

arxiv created 2012/12/19 · arxiv updated 2012/12/20

Abstract

In a filtered measure space, a characterization of weights for which the trace inequality of a positive operator holds is given by the use of discrete Wolff's potential. A refinement of the Carleson embedding theorem is also introduced. Sawyer type characterization of weights for which a two-weight norm inequality for a generalized Doob's maximal operator holds is established by an application of our Carleson embedding theorem. Moreover, Hytönen-Pérez type one-weight norm estimate for Doob's maximal operator is obtained by the use of our two-weight characterization.

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