Journal of Mathematical Sciences

, Volume 165, Issue 4, pp 483–490

Two remarks on the relationship between BMO-regularity and analytic stability of interpolation for lattices of measurable functions


We study in this paper Hardy-type spaces on a measure space (\( \mathbb{T} \), m) × (Ω, µ), where (\( \mathbb{T} \), m) is the unit circle with Lebesgue measure. There is a characterization of analytic stability for real interpolation of weighted Hardy spaces on \( \mathbb{T} \) × Ω, a complete proof of which was present in the literature only for the case where µ is a point mass. Here this gap is filled, and a proof of the general case is presented. In a previous work by Kislyakov, certain results concerning BMO-regular lattices on (\( \mathbb{T} \) × Ω, m × µ) were proved under the assumption that the measure µ is discrete. Here this extraneous assumption is lifted. Bibliography: 9 titles.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. Cwikel, J. E. McCarthy, and T. H. Wolf, “Interpolation between weighted Hardy spaces,” Proc. Amer. Math. Soc., 116, 381–388.Google Scholar
  2. 2.
    J. B. Garnett, Bounded Analytic Functions, Acad. Press, New York (1981).MATHGoogle Scholar
  3. 3.
    J. Bergh and J. Löfström, Interpolation Spaces. An Introduction, Springer-Verlag (1976).MATHGoogle Scholar
  4. 4.
    S. V. Kisliakov, “Interpolation of H p-spaces: some recent developments,” Israel Math. Conf. Proc., 13, 102–140 (1999).MathSciNetGoogle Scholar
  5. 5.
    S. V. Kisliakov and Xu Quanhua, “Interpolation of weighted and vetor-valued Hardy spaces,” Trans. Amer. Mat. Soc., 343, 1–34 (1994).MATHCrossRefGoogle Scholar
  6. 6.
    S. V. Kisliakov, “On BMO-regular lattices of measurable functions,” Algebra Analiz, 14, 117–135 (2002).Google Scholar
  7. 7.
    S. V. Kislyakov, “On BMO-regular couples of lattices of measurable functions,” Studia Mathematica, 159(2), 277–289 (2003).MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    I. I. Privalov, Boundary Properties of Analytic Functions [in Russian], Moscow (1950).Google Scholar
  9. 9.
    S. V. Kislyakov, “On BMO-regular lattices of measurable functions. II,” Zap. Nauchn. Semin. POMI, 303, 161–168 (2203).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  1. 1.St. Petersburg Department of Steklov Mathematical Institute RASSt. PetersburgRussia

Personalised recommendations