The Lizorkin-Freitag formula for several weighted $L_p$ spaces and vector-valued interpolation

Irina Asekritova, Natan Krugljak, and Ludmila Nikolova. "The Lizorkin-Freitag formula for several weighted $L_{p}$ spaces and vector-valued interpolation." Studia Mathematica 170.3 (2005): 227-239. <http://eudml.org/doc/286284>.

@article{IrinaAsekritova2005,
abstract = {A complete description of the real interpolation space $L = (L_\{p₀\}(ω₀),...,L_\{pₙ\}(ωₙ))_\{θ⃗,q\}$ is given. An interesting feature of the result is that the whole measure space (Ω,μ) can be divided into disjoint pieces $Ω_\{i\}$ (i ∈ I) such that L is an $l_\{q\}$ sum of the restrictions of L to $Ω_\{i\}$, and L on each $Ω_\{i\}$ is a result of interpolation of just two weighted $L_\{p\}$ spaces. The proof is based on a generalization of some recent results of the first two authors concerning real interpolation of vector-valued spaces.},
author = {Irina Asekritova, Natan Krugljak, Ludmila Nikolova},
journal = {Studia Mathematica},
keywords = {vector-valued interpolation; weighted spaces; Lizorkin-Freitag formula},
language = {eng},
number = {3},
pages = {227-239},
title = {The Lizorkin-Freitag formula for several weighted $L_\{p\}$ spaces and vector-valued interpolation},
url = {http://eudml.org/doc/286284},
volume = {170},
year = {2005},
}

TY - JOUR
AU - Irina Asekritova
AU - Natan Krugljak
AU - Ludmila Nikolova
TI - The Lizorkin-Freitag formula for several weighted $L_{p}$ spaces and vector-valued interpolation
JO - Studia Mathematica
PY - 2005
VL - 170
IS - 3
SP - 227
EP - 239
AB - A complete description of the real interpolation space $L = (L_{p₀}(ω₀),...,L_{pₙ}(ωₙ))_{θ⃗,q}$ is given. An interesting feature of the result is that the whole measure space (Ω,μ) can be divided into disjoint pieces $Ω_{i}$ (i ∈ I) such that L is an $l_{q}$ sum of the restrictions of L to $Ω_{i}$, and L on each $Ω_{i}$ is a result of interpolation of just two weighted $L_{p}$ spaces. The proof is based on a generalization of some recent results of the first two authors concerning real interpolation of vector-valued spaces.
LA - eng
KW - vector-valued interpolation; weighted spaces; Lizorkin-Freitag formula
UR - http://eudml.org/doc/286284
ER -