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## Studia Mathematica

2003 | 159 | 2 | 277-290
Tytuł artykułu

### On BMO-regular couples of lattices of measurable functions

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Języki publikacji
EN
Abstrakty
EN
We introduce a new "weak" BMO-regularity condition for couples (X,Y) of lattices of measurable functions on the circle (Definition 3, Section 9), describe it in terms of the lattice $X^{1/2}(Y')^{1/2}$, and prove that this condition still ensures "good" interpolation for the couple $(X_{A},Y_{A})$ of the Hardy-type spaces corresponding to X and Y (Theorem 1, Section 9). Also, we present a neat version of Pisier's approach to interpolation of Hardy-type subspaces (Theorem 2, Section 13). These two main results of the paper are proved in Sections 10-18, where some related material of independent interest is also discussed. Sections 1-8 are devoted to the background and motivations, and also include a short survey of some previously known results concerning BMO-regularity. To a certain extent, the layout of the paper models that of the lecture delivered by the author at the conference in functional analysis in honour of Aleksander Pełczyński (Bedlewo, September 22-29, 2002).
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Tom
Numer
Strony
277-290
Opis fizyczny
Daty
wydano
2003
Twórcy
autor
• Russian Academy of Sciences, Steklov Mathematical Institute, St. Petersburg Department, Fontanka 27, St. Petersburg 191023, Russia
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