Geodesic
$\omega $--weighted holomorphic Besov spaces on the unit ball in $C^n$
Commentationes Mathematicae Universitatis Carolinae, Tome 52 (2011) no. 1, pp. 37-56

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

The $\omega$-weighted Besov spaces of holomorphic functions on the unit ball $B^n$ in $C^n$ are introduced as follows. Given a function $\omega $ of regular variation and $0 p \infty $, a function $f$ holomorphic in $B^n$ is said to belong to the Besov space $B_p(\omega)$ if $$ \Vert f\Vert^p_{B_p(\omega )}=\int_{B^n} (1-|z|^2)^p|Df(z)|^p \frac{\omega(1-|z|)}{(1-|z|^2)^{n+1}}\,d\nu(z) +\infty , $$ where $d\nu (z)$ is the volume measure on $B^n$ and $D$ stands for the fractional derivative of $f$. The holomorphic Besov space is described in the terms of the corresponding $L_p(\omega )$ space. Some projection theorems and theorems on existence of the inversions of these projections are proved. Also, explicit descriptions of the duals of the considered Besov spaces are given.
Classification : 32C37, 46E15, 46T25, 47B38
Keywords: weighted Besov spaces; unit ball; projection 
@article{CMUC_2011__52_1_a3,
     author = {Harutyunyan, A. V. and Lusky, W.},
     title = {$\omega $--weighted holomorphic {Besov} spaces on the unit ball in $C^n$},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {37--56},
     publisher = {mathdoc},
     volume = {52},
     number = {1},
     year = {2011},
     mrnumber = {2828371},
     zbl = {1240.32017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2011__52_1_a3/}
}
TY  - JOUR
AU  - Harutyunyan, A. V.
AU  - Lusky, W.
TI  - $\omega $--weighted holomorphic Besov spaces on the unit ball in $C^n$
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2011
SP  - 37
EP  - 56
VL  - 52
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_2011__52_1_a3/
LA  - en
ID  - CMUC_2011__52_1_a3
ER  - 
%0 Journal Article
%A Harutyunyan, A. V.
%A Lusky, W.
%T $\omega $--weighted holomorphic Besov spaces on the unit ball in $C^n$
%J Commentationes Mathematicae Universitatis Carolinae
%D 2011
%P 37-56
%V 52
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_2011__52_1_a3/
%G en
%F CMUC_2011__52_1_a3
Harutyunyan, A. V.; Lusky, W. $\omega $--weighted holomorphic Besov spaces on the unit ball in $C^n$. Commentationes Mathematicae Universitatis Carolinae, Tome 52 (2011) no. 1, pp. 37-56. http://geodesic.mathdoc.fr/item/CMUC_2011__52_1_a3/