On BMO-regular couples of lattices of measurable functions

S. V. Kislyakov. "On BMO-regular couples of lattices of measurable functions." Studia Mathematica 159.2 (2003): 277-290. <http://eudml.org/doc/284855>.

@article{S2003,
abstract = {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 $X^\{1/2\}(Y^\{\prime \})^\{1/2\}$, 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).},
author = {S. V. Kislyakov},
journal = {Studia Mathematica},
keywords = {quasi-Banach lattice; BMO-regularity; analytically K-stable couple},
language = {eng},
number = {2},
pages = {277-290},
title = {On BMO-regular couples of lattices of measurable functions},
url = {http://eudml.org/doc/284855},
volume = {159},
year = {2003},
}

TY - JOUR
AU - S. V. Kislyakov
TI - On BMO-regular couples of lattices of measurable functions
JO - Studia Mathematica
PY - 2003
VL - 159
IS - 2
SP - 277
EP - 290
AB - 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 $X^{1/2}(Y^{\prime })^{1/2}$, 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).
LA - eng
KW - quasi-Banach lattice; BMO-regularity; analytically K-stable couple
UR - http://eudml.org/doc/284855
ER -