Maximal Functions Associated to Filtrations
Maximal Functions Associated to Filtrations
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DOI：
10.1006/jfan.2000.3687
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发表时间：
2001-02
影响因子：
1.7
通讯作者：
Michael Christ;A. Kiselev
中科院分区：
文献类型：
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作者：
Michael Christ;A. Kiselev
设T是从Lp（Y）到Lq（X）的有界线性或次线性算子.一个极大算子T*f（x）=supj| T（f·xYj）（x）|与Y的子集Yj的任何序列相关联。在q>p和集合Yj是嵌套的假设下，我们证明了T* 也是有界的.作为推论，得到了Menshov和Zygmund的经典定理。这个定理的多线性推广也成立。这些结果的动机的应用程序的薛定谔算子的谱分析。
Abstract Let T be a bounded linear, or sublinear, operator from Lp(Y) to Lq(X). A maximal operator T*f(x)=supj |T(f·χYj)(x)| is associated to any sequence of subsets Yj of Y. Under the hypotheses that q>p and the sets Yj are nested, we prove that T* is also bounded. Classical theorems of Menshov and Zygmund are obtained as corollaries. Multilinear generalizations of this theorem are also established. These results are motivated by applications to the spectral analysis of Schrodinger operators.