Positive operators and maximal operators in a filtered measure space
Positive operators and maximal operators in a filtered measure space
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DOI：
10.1016/j.jfa.2012.12.003
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发表时间：
2012-04
期刊：
影响因子：
--
通讯作者：
Hitoshi Tanaka;Yutaka Terasawa
中科院分区：
文献类型：
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作者：
Hitoshi Tanaka;Yutaka Terasawa
在滤子测度空间中，利用离散的WolffʼS势，给出了正算子的迹不等式成立的权重的一个刻划.还介绍了Carleson嵌入定理的一种改进。应用Carleson嵌入定理，建立了广义DoobʼS极大算子的两权范数不等式成立的权的Sawyer型刻画.此外，利用我们的双权刻画得到了DoobʼS极大算子的Hytönen-Pérez型单权范数估计。
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 Wolffʼs 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 Doobʼs maximal operator holds is established by an application of our Carleson embedding theorem. Moreover, Hytönen–Pérez type one-weight norm estimate for Doobʼs maximal operator is obtained by the use of our two-weight characterization.