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http://dx.doi.org/10.7858/eamj.2015.006

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)
Publication Information
East Asian mathematical journal / v.31, no.1, 2015 , pp. 55-63 More about this Journal
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 $\mathbb{B}$.
Keywords
division problem; generalized growth spaces; unit ball;
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