Maximal Functions Associated to Filtrations

  title={Maximal Functions Associated to Filtrations},
  author={Michael Christ and Alexander V. Kiselev},
  journal={Journal of Functional Analysis},
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. 

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  • A. ZygmundG. Hardy
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1936
1. Let f(x) be a complex function belonging to LP (−∞, ∞); i.e. let f(x) be measurable, and |f(x)|p integrable, over (−∞, ∞). The function is called the Fourier transform of f(x), if the integral on

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