East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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DIVISION PROBLEM IN GENERALIZED GROWTH SPACES ON THE UNIT BALL IN ℂn

  • Cho, Hong Rae (Department of Mathematics, Pusan National University) ;
  • Lee, Han-Wool (Department of Mathematics, Pusan National University) ;
  • Park, Soohyun (Department of Mathematics, Pusan National University)
  • Received : 2014.10.22
  • Accepted : 2014.12.09
  • Published : 2015.01.31
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Abstract

Let $\mathbb{B}$ be the unit ball in $\mathbb{C}^n$. For a weight function ${\omega}$, we define the generalized growth space $A^{\omega}(\mathbb{B})$ by the space of holomorphic functions f on $\mathbb{B}$ such that $${\mid}f(z){\mid}{\leq}C{\omega}({\mid}{\rho}(z){\mid},\;z{\in}\mathbb{B}$$. Our main purpose in this note is to get the corona type decomposition in generalized growth spaces on $\mathbb{B}$.

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References

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