NOTES ON THE BERGMAN PROJECTION TYPE OPERATOR IN ℂn

Title & Authors
NOTES ON THE BERGMAN PROJECTION TYPE OPERATOR IN ℂn
Choi, Ki-Seong;

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 $\small{L^p}$(B, dv). By using the properties of the Bergman projection type operator Pr, we will show that if $\small{f{\in}L_a^p}$(B, dv), then $\small{(1-{\parallel}{\omega}{\parallel}^2){\nabla}f(\omega){\cdot}z{\in}L^p(B,dv)}$. 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;
Language
English
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