The radial derivatives on weighted Bergman spaces

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 $z \in H$.