, Volume 165, Issue 4, pp 483-490
Date: 24 Feb 2010

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

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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.

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 366, 2009, pp. 102–115.