IJPAM: Volume 35, No. 2 (2007)

VANISHING CARLESON MEASURE ON
THE UNIT BALL IN $C^n$

Ki Seong Choi
Department of Information Security
Konyang University
Nonsan, 320-711, KOREA
e-mail: ksc@konyang.ac.kr


Abstract.Suppose that $\mu$ is a finite positive Borel measure on the unit ball $B \subset C^n$. In this paper, we will show that if the operator $T(f) = P[f]$ is compact as a mapping from $H^2
(\sigma)$ into $L^2 (B, d \mu)$, then $\mu$ is vanishing Carleson measure.

Received: December 23, 2006

AMS Subject Classification: 32H25, 32E25, 30C40

Key Words and Phrases: vanishing Carleson measure, Poisson-Szegö kernel

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 35
Issue: 2