Lions–Peetre reiteration formulas for triples
and their applications
Studia Mathematica, Tome 145 (2001) no. 3, pp. 219-254
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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 $(\theta ,q)$-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 $L_p(\mu )$-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.
Keywords:
present discuss apply reiteration theorems triples quasi banach function lattices interpolation results block lorentz spaces triples weighted p spaces proved using these results wavelet theory approach calculate theta spaces triples smooth function spaces besov spaces sobolev spaces etc contrast couples which even scale besov spaces stable under interpolation triples obtain stability frame besov spaces based lorentz spaces moreover using results ideas paper extend stein weiss interpolation theorem known spaces change measures lorentz spaces change measures particular results obtained problems analysis three space real interpolation approach really useful usual real interpolation between couples
Affiliations des auteurs :
Irina Asekritova 1 ; Natan Krugljak 2 ; Lech Maligranda 3 ; Lyudmila Nikolova 4 ; Lars-Erik Persson 3
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author = {Irina Asekritova and Natan Krugljak and Lech Maligranda and Lyudmila Nikolova and Lars-Erik Persson},
title = {Lions{\textendash}Peetre reiteration formulas for triples
and their applications},
journal = {Studia Mathematica},
pages = {219--254},
publisher = {mathdoc},
volume = {145},
number = {3},
year = {2001},
doi = {10.4064/sm145-3-4},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm145-3-4/}
}
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 SP - 219 EP - 254 VL - 145 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/sm145-3-4/ DO - 10.4064/sm145-3-4 LA - en ID - 10_4064_sm145_3_4 ER -
%0 Journal Article %A Irina Asekritova %A Natan Krugljak %A Lech Maligranda %A Lyudmila Nikolova %A Lars-Erik Persson %T Lions–Peetre reiteration formulas for triples and their applications %J Studia Mathematica %D 2001 %P 219-254 %V 145 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/sm145-3-4/ %R 10.4064/sm145-3-4 %G en %F 10_4064_sm145_3_4
Irina Asekritova; Natan Krugljak; Lech Maligranda; Lyudmila Nikolova; Lars-Erik Persson. Lions–Peetre reiteration formulas for triples and their applications. Studia Mathematica, Tome 145 (2001) no. 3, pp. 219-254. doi: 10.4064/sm145-3-4
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