Ces\`aro operators in the Bergman spaces with exponential weight on the unit ball
Bull. Korean Math. Soc. 2017 Vol. 54, No. 2, 705-714
Published online January 9, 2017
Printed March 31, 2017
Hong Rae Cho and Inyoung Park
Pusan National University, Pohang University of Science and Technology
Abstract : Let $A^2_{\alpha,\beta}(\Bn)$ denote the space of holomorphic functions that are $L^2$ with respect to a weight of form $\omega_{\alpha,\beta}(z)=(1-|z|)^\alpha e^{-\frac{\beta}{1-|z|}}$, where $\alpha\in\mathbb R$ and $\beta>0$ on the unit ball $\Bn$. We obtain some results for the boundedness and compactness of Ces\`aro operator on $A^2_{\alpha,\beta}(\Bn)$.
Keywords : Ces\`aro operators, Bergman spaces with exponential weight, unit ball
MSC numbers : 32A36, 47B38
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