Hankel and Toeplitz type operators on the unit disk  

作　　者：何建勋 彭立中 

出　　处：《Science China Mathematics》2002年第9期1154-1162,共9页中国科学：数学（英文版）

基　　金：This work was supported by the National Natural Science Foundation of China(Grant Nos. 10071039, 90104004 and 19872006); the 973 Project (Grant No. 1999075105) ; the Foundation of Educational Commission of Jiangsu Province, China.

摘　　要：Let D be the unit disk in the complex plane with the weighted measure $d\mu _\beta \left( z \right) = \frac{{\beta + 1}}{\pi }\left( {1 - \left| z \right|^2 } \right)^\beta dm\left( z \right)\left( {\beta > - 1} \right)$ . Then $L^2 \left( {D, d\mu _\beta \left( z \right)} \right) = \oplus _{k = 0}^\infty \left( {A_k^\beta \oplus \bar A_k^\beta } \right)$ is the orthogonal direct sum decomposition. In this paper, we define the Hankel and Toeplitz type operators, and study the boundedness, compactness and Sp-criteria for them.Let D be the unit disk in the complex plane with the weighted measure dμβ(z) = (β+1)--π(1-|z|2)βdm(z)(β＞-1). Then L2(D,dμβ(z)) = ∞k=0(Aβk Aβk) is the orthogonal direct sum decomposition.In this paper, we define the Hankel and Toeplitz type operators, and study the boundedness, compactness and Sp-criteria for them.

关 键 词：HANKEL TYPE operator  TOEPLITZ TYPE operator  Sp-criteria  ANALYTIC BESOV space  para-commutator. 

分 类 号：O177[理学—数学]