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 , and prove that this condition still ensures “good” interpolation for the couple 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).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm159-2-8,
author = {S. V. Kislyakov},
title = {On BMO-regular couples of lattices of measurable functions},
journal = {Studia Mathematica},
volume = {157},
year = {2003},
pages = {277-290},
zbl = {1063.46014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm159-2-8}
}
S. V. Kislyakov. On BMO-regular couples of lattices of measurable functions. Studia Mathematica, Tome 157 (2003) pp. 277-290. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm159-2-8/