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.

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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 
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     title = {$\omega $--weighted holomorphic {Besov} spaces on the unit ball in $C^n$},
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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/