Commun. Korean Math. Soc. 2003; 18(3): 469-479
Printed September 1, 2003
Copyright © The Korean Mathematical Society.
Ki Seong Choi
Konyang university
Let $B$ be the open unit ball in $\Bbb C^n$ and $\mu_q (q> -1)$ the Lebesgue measure such that $\mu_q (B) = 1$. Let $L^2_{a, q}$ be the subspace of $L^2 (B, d {\mu}_q )$ consisting of analytic functions, and let $\overline{L^2_{a,q}}$ be the subspace of $L^2 (B, d \mu_q )$ consisting of conjugate analytic functions. Let $\overline{P}$ be the orthogonal projection from $L^2 (B, d\mu_q )$ into $\overline{L^2_{a, q}}$. The little Hankel operator $h^q_{\varphi} : L^2_{a,q} \rightarrow \overline{L^2_{a,q}}$ is defined by $h_{{\varphi}}^q (\cdot )= \overline{P} (\varphi \ \cdot) $. In this paper, we will find the necessary and sufficient condition that the little Hankel operator $h^q_{\varphi}$ is bounded(or compact).
Keywords: Bergman space, little Hankel operator, weighted Bloch space
MSC numbers: 32H25, 32E25, 30C40
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