# SOME DUALITY OF WEIGHTED BERGMAN SPACES OF THE HALF-PLANE

• Published : 2005.05.01
• 42 3

#### Abstract

In the setting of the half-plane of the complex plane, we introduce a modified reproducing kernel and we show that for $r>-1/2,\;B^{1,r}-cancellation$ property holds and the Bloch space is the dual space of $B^{1,r}$.

#### Keywords

dual space, weighted Bergman space;modified Bergman kernels;half-plane;radial derivatives;Mobius transform

#### References

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2. H. Hedenmalm, B. Korenblum, and K. Zhu, Theory of Bergman spaces, Springer-Verlag, New York, 2000
3. S. H. Kang, Weighted Bloch spaces and some operators induced by radial derivatives, to appear
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5. J. Y. Kim, Weighted analytic Bergman spaces of the half plane and their Toeplitz operators, Ph. D. Thesis, Sookmyung Women's University, 2001

#### 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