Article

Journal of Mathematical Sciences

, Volume 165, Issue 4, pp 483-490

First online:

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

  • D. V. RutskyAffiliated withSt. Petersburg Department of Steklov Mathematical Institute RAS Email author 

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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.