On BMO-regular couples of lattices of measurable functions

• Autorzy: S. V. Kislyakov
• 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).

Kategorie tematyczne

• 46B70: Interpolation between normed linear spaces
• 46E25: Rings and algebras of continuous, differentiable or analytic functions
• 42B30: H p -spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 159
• Numer: 2
• Strony: 277-290

Daty

wydano

2003

Twórcy

autor

S. V. Kislyakov

• Russian Academy of Sciences, Steklov Mathematical Institute, St. Petersburg Department, Fontanka 27, St. Petersburg 191023, Russia

Identyfikatory

DOI

10.4064/sm159-2-8