DOI QR코드

DOI QR Code

SOME DUALITY OF WEIGHTED BERGMAN SPACES OF THE HALF-PLANE

  • Published : 2005.05.01

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

  1. S. Axler, P. Bourdon, and W. Ramey, Harmonic function theory, Springer-Verlag, New York, 1992
  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
  4. S. H. Kang and J. Y. Kim, The radial derivatives on weighted Bergman spaces, Commun. Korean Math. Soc. 18 (2003), no. 2, 243-249 https://doi.org/10.4134/CKMS.2003.18.2.243
  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