Jacobi polynomials and toeplitz-hankel type operators^∗

^∗Research was supported by the National Natural Science Foundation of China.

Abstract

Let L ²(D,dμ_α )(α > -1) be the space of square integrable functions on the unit disk D of complex plane with respect to the weighted measure . From the view point of the Cauchy-Riemann operator d/d [zbar] and group representation we construct an orthogonal decomposition via the Jacobi polynomials such that A ₀. and Ā ₀ are just the (weighted) Bergman and anti-Bergman spaces respectively. Then we define three kinds of lbeplitz and Hankel type operators and develop boundedness, compactness and S_p -criteria for them.

AMS No:

• 47B10
• 47B35
• 33C20
• 33C45

^∗Research was supported by the National Natural Science Foundation of China.

^∗Research was supported by the National Natural Science Foundation of China.

Notes

^∗Research was supported by the National Natural Science Foundation of China.