Toeplitz Operators on Bergman Spaces Defined on Upper Planes

Si Ho Kang; Ja Young Kim

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Commun. Korean Math. Soc. 1999; 14(1): 171-177

Printed March 1, 1999

Toeplitz Operators on Bergman Spaces Defined on Upper Planes

Si Ho Kang, Ja Young Kim

Sookmyung Women's University, Sookmyung Women's University

Abstract

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Abstract

We study some properties of Toeplitz operators on the Bergman spaces $B^{p}(H_{r})$, where $H_{r}= \{ x+iy : y > r \}$. We consider the pseudo-hyperbolic disk and the covering property. We also obtain some characterizations of compact Toeplitz operators.

Keywords: Toeplitz operators, Bergman spaces, upper plane, pseudo-hyperbolic disk

MSC numbers: Primary 47B35, 47B38; Secondary 31B10, 30D55