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http://dx.doi.org/10.4134/BKMS.b160288

CESÀRO OPERATORS IN THE BERGMAN SPACES WITH EXPONENTIAL WEIGHT ON THE UNIT BALL  

Cho, Hong Rae (Department of Mathematics Pusan National University)
Park, Inyoung (Center for Geometry and its Applications Pohang University of Science and Technology)
Publication Information
Bulletin of the Korean Mathematical Society / v.54, no.2, 2017 , pp. 705-714 More about this Journal
Abstract
Let $A^2_{{\alpha},{\beta}}(\mathbb{B}_n)$ denote the space of holomorphic functions that are $L^2$ with respect to a weight of form ${\omega}_{{\alpha},{\beta}}(z)=(1-{\mid}z{\mid}^{\alpha}e^{-{\frac{\beta}{1-{\mid}z{\mid}}}}$, where ${\alpha}{\in}\mathbb{R}$ and ${\beta}$ > 0 on the unit ball $\mathbb{B}_n$. We obtain some results for the boundedness and compactness of $Ces{\grave{a}}ro$ operator on $A^2_{{\alpha},{\beta}(\mathbb{B}_n)$.
Keywords
$Ces{\grave{a}}ro$ operators; Bergman spaces with exponential weight; unit ball;
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