Lions-Peetre reiteration formulas for triples and their applications

Irina Asekritova, et al. "Lions-Peetre reiteration formulas for triples and their applications." Studia Mathematica 145.3 (2001): 219-254. <http://eudml.org/doc/284442>.

@article{IrinaAsekritova2001,
abstract = {We present, discuss and apply two reiteration theorems for triples of quasi-Banach function lattices. Some interpolation results for block-Lorentz spaces and triples of weighted $L_\{p\}$-spaces are proved. By using these results and a wavelet theory approach we calculate (θ,q)-spaces for triples of smooth function spaces (such as Besov spaces, Sobolev spaces, etc.). In contrast to the case of couples, for which even the scale of Besov spaces is not stable under interpolation, for triples we obtain stability in the frame of Besov spaces based on Lorentz spaces. Moreover, by using the results and ideas of this paper, we can extend the Stein-Weiss interpolation theorem known for $L_\{p\}(μ)$-spaces with change of measures to Lorentz spaces with change of measures. In particular, the results obtained show that for some problems in analysis the three-space real interpolation approach is really more useful than the usual real interpolation between couples.},
author = {Irina Asekritova, Natan Krugljak, Lech Maligranda, Lyudmila Nikolova, Lars-Erik Persson},
journal = {Studia Mathematica},
keywords = {Banach function lattices; reiteration; block-Lorentz spaces; weighted -spaces; interpolation; wavelets; triples; stability},
language = {eng},
number = {3},
pages = {219-254},
title = {Lions-Peetre reiteration formulas for triples and their applications},
url = {http://eudml.org/doc/284442},
volume = {145},
year = {2001},
}

TY - JOUR
AU - Irina Asekritova
AU - Natan Krugljak
AU - Lech Maligranda
AU - Lyudmila Nikolova
AU - Lars-Erik Persson
TI - Lions-Peetre reiteration formulas for triples and their applications
JO - Studia Mathematica
PY - 2001
VL - 145
IS - 3
SP - 219
EP - 254
AB - We present, discuss and apply two reiteration theorems for triples of quasi-Banach function lattices. Some interpolation results for block-Lorentz spaces and triples of weighted $L_{p}$-spaces are proved. By using these results and a wavelet theory approach we calculate (θ,q)-spaces for triples of smooth function spaces (such as Besov spaces, Sobolev spaces, etc.). In contrast to the case of couples, for which even the scale of Besov spaces is not stable under interpolation, for triples we obtain stability in the frame of Besov spaces based on Lorentz spaces. Moreover, by using the results and ideas of this paper, we can extend the Stein-Weiss interpolation theorem known for $L_{p}(μ)$-spaces with change of measures to Lorentz spaces with change of measures. In particular, the results obtained show that for some problems in analysis the three-space real interpolation approach is really more useful than the usual real interpolation between couples.
LA - eng
KW - Banach function lattices; reiteration; block-Lorentz spaces; weighted -spaces; interpolation; wavelets; triples; stability
UR - http://eudml.org/doc/284442
ER -