Essential Norm of the Extended Ces\`{a}ro Operators on Bergman Spaces with Exponential Weight in the Unit Ball
Abstract
Let $\BB_n=\{z\in\C^n:|z|<1\}$ be the unit ball of the complex $n$-plane $\C^n$, $g$ a holomorphic function in $\BB_n$,
and $A^2_{\a,\b}(\BB_n)$ the space of holomorphic functions that are $L^2$ with respect to a rapidly decreasing weight of form $\omega_{\a,\b}(z)=(1-|z|)^\a e^{-\frac{\b}{1-|z|}}$
on $\BB_n$, where $\a\in\R$ and $\b>0$.
In this paper, we compute the essential norm of the extended Ces\`{a}ro operator $T_g$ on $A^2_{\a,\b}(\BB_n)$.
As a direct application, we obtain the essential norm for the one-variable case.
and $A^2_{\a,\b}(\BB_n)$ the space of holomorphic functions that are $L^2$ with respect to a rapidly decreasing weight of form $\omega_{\a,\b}(z)=(1-|z|)^\a e^{-\frac{\b}{1-|z|}}$
on $\BB_n$, where $\a\in\R$ and $\b>0$.
In this paper, we compute the essential norm of the extended Ces\`{a}ro operator $T_g$ on $A^2_{\a,\b}(\BB_n)$.
As a direct application, we obtain the essential norm for the one-variable case.
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