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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)
  • Received : 2016.04.04
  • Published : 2017.03.31

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 $A^2_{{\alpha},{\beta}(\mathbb{B}_n)$.

Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

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