A complete description of the real interpolation space is given. An interesting feature of the result is that the whole measure space (Ω,μ) can be divided into disjoint pieces (i ∈ I) such that L is an sum of the restrictions of L to , and L on each is a result of interpolation of just two weighted spaces. The proof is based on a generalization of some recent results of the first two authors concerning real interpolation of vector-valued spaces.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm170-3-2,
author = {Irina Asekritova and Natan Krugljak and Ludmila Nikolova},
title = {The Lizorkin-Freitag formula for several weighted $L\_{p}$ spaces and vector-valued interpolation},
journal = {Studia Mathematica},
volume = {166},
year = {2005},
pages = {227-239},
zbl = {1090.46013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm170-3-2}
}
Irina Asekritova; Natan Krugljak; Ludmila Nikolova. The Lizorkin-Freitag formula for several weighted $L_{p}$ spaces and vector-valued interpolation. Studia Mathematica, Tome 166 (2005) pp. 227-239. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm170-3-2/