For two kind of MSebius invariant subspace A^α,d（D） and A^β,2 （D）, define the Toeplitz operators Tf^s and Hankel operators Hf^r on A^α,d（D）×A^β,2 （D） with an arbi-trary analytic ＂symbol function＂ f ...For two kind of MSebius invariant subspace A^α,d（D） and A^β,2 （D）, define the Toeplitz operators Tf^s and Hankel operators Hf^r on A^α,d（D）×A^β,2 （D） with an arbi-trary analytic ＂symbol function＂ f on a unit disk, and study their boundedness, compactness and Schatten-von Neumann properties.展开更多
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} \r...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.展开更多
For two kinds of the Moebius invariant subspace A_l^(a,2)(D) and A_l^(-a,2)(D) of L^(a,2)(D), we define big and small Hankel operators H_b^(ll') and h_b^(ll') for the analytic symbol function b(z), and st...For two kinds of the Moebius invariant subspace A_l^(a,2)(D) and A_l^(-a,2)(D) of L^(a,2)(D), we define big and small Hankel operators H_b^(ll') and h_b^(ll') for the analytic symbol function b(z), and study their boundedness, compactness and Schatten-von Neumanu classes S_p-estimates, and hence develope Schatten -von Neumann properties of these op- erators.展开更多
文摘For two kind of MSebius invariant subspace A^α,d（D） and A^β,2 （D）, define the Toeplitz operators Tf^s and Hankel operators Hf^r on A^α,d（D）×A^β,2 （D） with an arbi-trary analytic ＂symbol function＂ f on a unit disk, and study their boundedness, compactness and Schatten-von Neumann properties.
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.
文摘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.
文摘For two kinds of the Moebius invariant subspace A_l^(a,2)(D) and A_l^(-a,2)(D) of L^(a,2)(D), we define big and small Hankel operators H_b^(ll') and h_b^(ll') for the analytic symbol function b(z), and study their boundedness, compactness and Schatten-von Neumanu classes S_p-estimates, and hence develope Schatten -von Neumann properties of these op- erators.
