Little Hankel operators on Weighted Bloch spaces in $\Bbb C^n$

Abstract

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).