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THE RADIAL DERIVATIVES ON WEIGHTED BERGMAN SPACES

Kang, Si-Ho;Kim, Ja-Young

  • Published : 2003.04.01

Abstract

We consider weighted Bergman spaces and radial derivatives on the spaces. We also prove that for each element f in B$\^$p, r/ there is a unique f in B$\^$p, r/ such that f is the radial derivative of f and for each f$\in$B$\^$r/(i), f is the radial derivative of some element of B$\^$r/(i) if and only if, lim f(tz)= 0 for all z$\in$H.

Keywords

weighted Bergman spaces;Bergman kernels;half-plane;radial derivatives

References

  1. Harmonic Bergman Fuctions as Radical Derivatives of Bergman Functions, Preprint B.R.Choe;H.Koo;H.Yi
  2. Harmonic Function Theory S.Axler;P.Bourdon;W.Ramey
  3. Pitman Research Notes in Math. v.171 Beryman Spaces and Their Operators, Surveys of Some Recent Results in Operator Theory Vol. 1. S. Axler
  4. Operator Theory in Function Spaces K.Zhu
  5. Bull. Korean Math. Soc. v.37 no.3 Toeplitz operators on weighted alalytic Beryman spaces of the half-plane S.H.Kang;J.Y.Kim
  6. Bounded Analytic Functions J.B.Garnett

Cited by

  1. Composition operators from the weighted Bergman space to the nth weighted-type space on the upper half-plane vol.217, pp.7, 2010, https://doi.org/10.1016/j.amc.2010.09.001