Maximal functions associated to filtrations

Journal Article (Journal Article)

Let T be a bounded linear, or sublinear, operator from Lp(Y) to Lq(X). A maximal operator T*f(x)=supjT(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 Schrödinger operators. © 2001 Academic Press.

Full Text

Duke Authors

Cited Authors

  • Christ, M; Kiselev, A

Published Date

  • February 1, 2001

Published In

Volume / Issue

  • 179 / 2

Start / End Page

  • 409 - 425

International Standard Serial Number (ISSN)

  • 0022-1236

Digital Object Identifier (DOI)

  • 10.1006/jfan.2000.3687

Citation Source

  • Scopus