Geodesic
The Stein–Weiss theorem for the ergodic Hilbert transform
Lasha Ephremidze 1
1 A. Razmadze Mathematical Institute 1, M. Aleksidze Str. 380093 Tbilisi, Georgia
Studia Mathematica, Tome 165 (2004) no. 1, pp. 61-71 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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The Stein–Weiss theorem that the distribution function of the Hilbert transform of the characteristic function of $E$ depends only on the measure of $E$ is generalized for the ergodic Hilbert transform in the case of a one-parameter flow of measure-preserving transformations on a $\sigma $-finite measure space.
DOI : 10.4064/sm165-1-5
Mots-clés : stein weiss theorem distribution function hilbert transform characteristic function depends only measure generalized ergodic hilbert transform one parameter flow measure preserving transformations sigma finite measure space

Lasha Ephremidze  1

1 A. Razmadze Mathematical Institute 1, M. Aleksidze Str. 380093 Tbilisi, Georgia 
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Lasha Ephremidze. The Stein–Weiss theorem for the
  ergodic Hilbert transform. Studia Mathematica, Tome 165 (2004) no. 1, pp. 61-71. doi: 10.4064/sm165-1-5

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