Abstract
Let B be the open unit ball in <TEX>$C^{n}$</TEX> and <TEX>${\mu}_{q}$</TEX>(q > -1) the Lebesgue measure such that <TEX>${\mu}_{q}$</TEX>(B) ＝ 1. Let <TEX>${L_{a,q}}^2$</TEX> be the subspace of <TEX>${L^2(B,D{\mu}_q)$</TEX> consisting of analytic functions, and let <TEX>$\overline{{L_{a,q}}^2}$</TEX> be the subspace of <TEX>${L^2(B,D{\mu}_q)$</TEX>) consisting of conjugate analytic functions. Let <TEX>$\bar{P}$</TEX> be the orthogonal projection from <TEX>${L^2(B,D{\mu}_q)$</TEX> into <TEX>$\overline{{L_{a,q}}^2}$</TEX>. The little Hankel operator <TEX>${h_{\varphi}}^{q}\;:\;{L_{a,q}}^2\;{\rightarrow}\;{\overline}{{L_{a,q}}^2}$</TEX> is defined by <TEX>${h_{\varphi}}^{q}(\cdot)\;=\;{\bar{P}}({\varphi}{\cdot})$</TEX>. In this paper, we will find the necessary and sufficient condition that the little Hankel operator <TEX>${h_{\varphi}}^{q}$</TEX> is bounded(or compact).
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