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.
L2 estimates are obtained for some oscillatory singular integral operators with analytic phrases by using the technology of almost orthogonality, oscillatory estimates and size estimates.
