Geodesic
A Carlson type inequality with blocks and interpolation
Studia Mathematica, Tome 104 (1993) no. 2, pp. 161-180

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

An inequality, which generalizes and unifies some recently proved Carlson type inequalities, is proved. The inequality contains a certain number of "blocks" and it is shown that these blocks are, in a sense, optimal and cannot be removed or essentially changed. The proof is based on a special equivalent representation of a concave function (see [6, pp. 320-325]). Our Carlson type inequality is used to characterize Peetre's interpolation functor $〈〉_{φ}$ (see [26]) and its Gagliardo closure on couples of functional Banach lattices in terms of the Calderón-Lozanovskiǐ construction. Our interest in this functor is inspired by the fact that if $φ = t^{θ}(0 θ 1)$, then, on couples of Banach lattices and their retracts, it coincides with the complex method (see [20], [27]) and, thus, it may be regarded as a "real version" of the complex method.
DOI : 10.4064/sm-104-2-161-180
Keywords: concavity, Carlson's inequality, blocks, interpolation, Peetre's interpolation functor, Calderón-Lozanovskiǐ construction

Natan Ya Kruglyak 1

1 
@article{10_4064_sm_104_2_161_180,
     author = {Natan Ya Kruglyak},
     title = {A {Carlson} type inequality with blocks and interpolation},
     journal = {Studia Mathematica},
     pages = {161--180},
     publisher = {mathdoc},
     volume = {104},
     number = {2},
     year = {1993},
     doi = {10.4064/sm-104-2-161-180},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-104-2-161-180/}
}
TY  - JOUR
AU  - Natan Ya Kruglyak
TI  - A Carlson type inequality with blocks and interpolation
JO  - Studia Mathematica
PY  - 1993
SP  - 161
EP  - 180
VL  - 104
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm-104-2-161-180/
DO  - 10.4064/sm-104-2-161-180
LA  - en
ID  - 10_4064_sm_104_2_161_180
ER  - 
%0 Journal Article
%A Natan Ya Kruglyak
%T A Carlson type inequality with blocks and interpolation
%J Studia Mathematica
%D 1993
%P 161-180
%V 104
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/sm-104-2-161-180/
%R 10.4064/sm-104-2-161-180
%G en
%F 10_4064_sm_104_2_161_180
Natan Ya Kruglyak. A Carlson type inequality with blocks and interpolation. Studia Mathematica, Tome 104 (1993) no. 2, pp. 161-180. doi: 10.4064/sm-104-2-161-180

Cité par Sources :