Boundedness of the Hausdorff operators in $H^p$ spaces, $0< p< 1$

Volume 194 / 2009

Elijah Liflyand, Akihiko Miyachi Studia Mathematica 194 (2009), 279-292 MSC: 42A38, 42B30. DOI: 10.4064/sm194-3-4

Abstract

Sufficient conditions for the boundedness of the Hausdorff operators in the Hardy spaces $H^p$, $0< p < 1$, on the real line are proved. Two related negative results are also given.

Authors

  • Elijah LiflyandDepartment of Mathematics
    Bar-Ilan University
    Ramat-Gan 52900, Israel
    e-mail
  • Akihiko MiyachiDepartment of Mathematics
    Tokyo Woman's Christian University
    Zempukuji, Suginami-ku
    Tokyo 167-8585, Japan
    e-mail

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