# SOME OPERATORS ON THE WEIGHTED BERGMAN SPACES

• Accepted : 2008.03.06
• Published : 2008.03.25
• 52 11

#### Abstract

In the setting of the half-plane of the complex plane, we show that for r > $-{\frac{1}{2}}$, the dual space of the weighted Bergman spaces $B^{1,r}$ is the Bloch space and we introduce some operators. We also study Toeplitz and Hankel operators and we find some characterization of Hankel operators.

#### Keywords

Dual space;weighted Bergman space;$B^{1,r}$-cancellation property;Toeplitz operators;Hankel operators

#### References

1. S.Axler, The Bergman Space, The Bloch Space, and Commutators of Multiplication Operators, Duke Math. J. Vol. 53, No.2 (1986), 315-332. https://doi.org/10.1215/S0012-7094-86-05320-2
2. S.G.Gindkin, Analysis in Homogeneous Domains, Usp. Matern. Nauk 19, No.4 (1964), 1-88.
3. H. Hedenmalm, B.Korenblum, and K.zhu, Theory of Bergman Spaces, Springer-Verlag, Inc., New York, 2000.
4. J.Y.Kim, Weighted Analytic Bergman Spaces of the Half Plane and Their Toeplitz Operators, Ph.D. Thesis, Sookmyung Women's University, 2000.
5. K.Zhu, Operator Theory in Function Spaces, Marcel Dekker, Inc., New York and Basel, 1990.

#### Cited by

1. On Toeplitz Operators on the Weighted Harmonic Bergman Space on the Upper Half-Plane vol.9, pp.1, 2015, https://doi.org/10.1007/s11785-014-0388-9