$\omega$–weighted holomorphic Besov spaces on the unit ball in $C^n$

@article{Harutyunyan2011,
abstract = {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.},
author = {Harutyunyan, A. V., Lusky, Wolfgang},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {weighted Besov spaces; unit ball; projection; weighted Besov space; unit ball; projection; holomorphic function},
language = {eng},
number = {1},
pages = {37-56},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {$\omega $–weighted holomorphic Besov spaces on the unit ball in $C^n$},
url = {http://eudml.org/doc/246848},
volume = {52},
year = {2011},
}

TY - JOUR
AU - Harutyunyan, A. V.
AU - Lusky, Wolfgang
TI - $\omega $–weighted holomorphic Besov spaces on the unit ball in $C^n$
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2011
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 52
IS - 1
SP - 37
EP - 56
AB - 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.
LA - eng
KW - weighted Besov spaces; unit ball; projection; weighted Besov space; unit ball; projection; holomorphic function
UR - http://eudml.org/doc/246848
ER -