We consider the hyponormality of the block dual Toeplitz operator S_(Φ)acting on the orthogonal complement of the vector valued weighted Bergman space (A_(α)^(2)(D,C^(n)))^(⊥).We provide a necessary and sufficient ...We consider the hyponormality of the block dual Toeplitz operator S_(Φ)acting on the orthogonal complement of the vector valued weighted Bergman space (A_(α)^(2)(D,C^(n)))^(⊥).We provide a necessary and sufficient condition for the hyponormality of SΦwith matrix valued bounded harmonic symbol.In this process,we introduce a function g_(w,s)∈(A_(α)^(2)(D))^(⊥),which is similar to the reproducing kernel of the weighted Bergman space A_(α)^(2)(D).We also give some additional applications of the function gw,s∈(A_(α)^(2)(D))^(⊥).展开更多
基金Supported by the Scientific Research Fund of Liaoning Provincial Education Department of China (Grant No.LJKMZ20221405)the National Natural Science Foundation of China (Grant No.12031002)。
文摘We consider the hyponormality of the block dual Toeplitz operator S_(Φ)acting on the orthogonal complement of the vector valued weighted Bergman space (A_(α)^(2)(D,C^(n)))^(⊥).We provide a necessary and sufficient condition for the hyponormality of SΦwith matrix valued bounded harmonic symbol.In this process,we introduce a function g_(w,s)∈(A_(α)^(2)(D))^(⊥),which is similar to the reproducing kernel of the weighted Bergman space A_(α)^(2)(D).We also give some additional applications of the function gw,s∈(A_(α)^(2)(D))^(⊥).
