논문KCI 등재
Ces\`aro operators in the Bergman spaces with exponential weight on the unit ball
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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 $A^2_{\alpha,\beta}(\Bn)$.
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 $A^2_{\alpha,\beta}(\Bn)$.
참고문헌 (10)
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- M. Dostani´c, "Integration operators on Bergman spaces with exponential weight", Rev. Mat. Iberoamericana, 23(2), pp.421~436 (2007)
- P. Lin, "Hankel operators on the weighted Bergman spaces with expo-nential type weights", Integral Equatons Operator Theory, 21(4), pp.460~483 (1995)
- M. Pavlovi´c, "An equivalence for weighted integrals of an analytic function and its derivative", Math. Nachr, 281(11), pp.1612~1623 (2008)
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