一类Hankel算子与Toeplitz算子的Sp性质

对于L~(α,2)(D))的两类Moebius不变子空间A~(α,2)(D)和A~(β,2)(D),我们定义了它们之间的Toeplitz算子T_f~s与其乘积空间上的Hankel算子H_f~r,并且研究了它们的有界性、紧性及Schatten-von Neumann性质。

The Sp Property of a kind of Hankel Operators and Toeplitz Operators

For two kind of M\"{o}ebius invariant subspace $A^{\alpha,2} \left( {D} \right)$ and $A^{\beta ,2} \left( {D} \right)$ of $L^{\alpha ,2} \left( {D} \right)$, define the Toeplitz operators $T_{f}^{s}$ and Hankel operators $H_{f}^{r} $ on $A^{\alpha ,2} \left({D} \right)\times A^{\beta ,2} \left( {D} \right)$ with an arbitrary analytic ``symbol function' $f$ on a unit disk, and study their boundedness, compactness and Schatten-von Neumann properties.