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Maximal Functions Associated to Filtrations

✍ Scribed by Michael Christ; Alexander Kiselev

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
163 KB
Volume
179
Category
Article
ISSN
0022-1236

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✦ Synopsis

Let T be a bounded linear, or sublinear, operator from L p (Y) to L q (X ). A maximal operator T *f (x)=sup j |T( f } / Y j )(x)| is associated to any sequence of subsets Y j of Y. Under the hypotheses that q>p and the sets Y j 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 Schro dinger operators.

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