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arXiv · 1204.6600

Positive operators and maximal operators in a filtered measure space

Hitoshi Tanaka·Yutaka Terasawa
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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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Hitoshi Tanaka, Yutaka Terasawa. 2012-12-19. Positive operators and maximal operators in a filtered measure space. https://arxiv.org/abs/1204.6600

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