The radial derivatives on weighted Bergman spaces
Commun. Korean Math. Soc. 2003 Vol. 18, No. 2, 243-249
Printed June 1, 2003
Si Ho Kang, Ja Young Kim
Sookmyung Women's University, Sookmyung Women's University
Abstract : We consider weighted Bergman spaces and radial deri-vatives on the spaces. We also prove that for each element $f$ in $B^{p,r}$, there is a unique $\widetilde{f}$ in $B^{p,r}$ such that $f$ is the radial derivative of $\widetilde{f}$ and for each $f \in \mathcal{B}^{r}(i)$, $f$ is the radial derivative of some element of $\mathcal{B}^{r}(i)$ if and only if $\displaystyle \lim_{t \to \infty} f(tz) = 0$ for all $z \in H$.
Keywords : weighted Bergman spaces, Bergman kernels, half-plane, radial derivatives
MSC numbers : Primary 31B05, 31B10; Secondary 32A36
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