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http://dx.doi.org/10.4134/CKMS.2006.21.1.065

NOTES ON THE BERGMAN PROJECTION TYPE OPERATOR IN ℂn  

Choi, Ki-Seong (Department of Information Security Konyang University)
Publication Information
Communications of the Korean Mathematical Society / v.21, no.1, 2006 , pp. 65-74 More about this Journal
Abstract
In this paper, we will define the Bergman projection type operator Pr and find conditions on which the operator Pr is bound-ed on $L^p$(B, dv). By using the properties of the Bergman projection type operator Pr, we will show that if $f{\in}L_a^p$(B, dv), then $(1-{\parallel}{\omega}{\parallel}^2){\nabla}f(\omega){\cdot}z{\in}L^p(B,dv)$. We will also show that if $(1-{\parallel}{\omega}{\parallel}^2)\; \frac{{\nabla}f(\omega){\cdot}z}{},\;{\in}L^p{B,\;dv),\;then\;f{\in}L_a^p(B,\;dv)$.
Keywords
Bergman space; Bergman projection;
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Times Cited By KSCI : 2  (Citation Analysis)
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