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A BMO type characterization of weighted Lipschitz functionsin terms of the Berezin transform

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Abstract

The Berezin transform is the analogue of the Poissontransform in the Bergman spaces.Dyakonov characterize the holomorphic weighted Lipschitz functionin the unit disk in terms of the Poisson integral.In this paper, we characterize the harmonic weighted Lipschitz functionin terms of the Berezin transform instead of the Poisson integral.

참고문헌 (15)

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  4. "Atomic decomposition of generalized Lipschitz spaces" (1989)
  5. "Weighted Lipschitz spaces and their analyticcharacterizations" (1994)
  6. "Derivatives of Harmonic Bergman and Bloch functions on theball" (2001)
  7. "Equivalent norms on Lipschitz-type spaces of holomorphicfunctions" (1997)
  8. "Holomorphic functions and quasiconformal mappings withsmooth moduli" (2004)
  9. "Strong Hardy-Littlewood theorems for analytic functionsand mappings of finite distortion" (2005)
  10. "Theory of Bergman spaces" (2000)
  11. "On Dyakonov spaper Equivalent norms on Lipschitz-type spaces of holomorphicfunctions" (1999)
  12. "Introduction to Function Spaces on the Disk" (2004)
  13. "Function theory in the unit ball ofmathbb" (1980), Springer-Verlag Press
  14. "operators on the Bergman space" (1987)
  15. "Operator Theory in Function Spaces" (1990)

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