Positive operators and maximal operators in a filtered measure space
Classical Analysis and ODEs
2012-12-20 v3 Probability
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, Hyt\"{o}nen-P\'{e}rez type one-weight norm estimate for Doob's maximal operator is obtained by the use of our two-weight characterization.
Cite
@article{arxiv.1204.6600,
title = {Positive operators and maximal operators in a filtered measure space},
author = {Hitoshi Tanaka and Yutaka Terasawa},
journal= {arXiv preprint arXiv:1204.6600},
year = {2012}
}
Comments
23 pages; v2:Typos corrected, v3:Typos corrected, references added. To appear in Journal of Functional Analysis