대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제21권3호
  • /
  • Pages.419-428
  • /
  • 2006
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

A BMO TYPE CHARACTERIZATION OF WEIGHTED LIPSCHITZ FUNCTIONS IN TERMS OF THE BEREZIN TRANSFORM

  • Cho, Hong-Rae (Department of Mathematics Pusan National University) ;
  • Seo, Yeoung-Tae (Department of Mathematics Pusan National University)
  • 발행 : 2006.07.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

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

키워드

참고문헌

  1. P. Ahern, M. Flores and W. Rudin, An invariant volume-mean value Property, J. Funct. Anal. 111 (1993), 380-397 https://doi.org/10.1006/jfan.1993.1018
  2. Bekolle, Berger, Coburn, and Zhu, BMO in the Bergman metric on bounded symmetric domains, J. Func. Anal. 93 (1990), 310-350 https://doi.org/10.1016/0022-1236(90)90131-4
  3. F. A. Berezin, Covariant and contravariant symbols of operators, Math. USSR-Izv.6 (1972), 1117-1151 https://doi.org/10.1070/IM1972v006n05ABEH001913
  4. F. A. Berezin, The relation between covariant and contravariant symbols of operators on classical complex symmetric spaces, Soviet Math. Dokl. 19 (1978), 786-789
  5. S. Bloom and G. S. De Souza, Atomic decomposition of generalized Lipschitz spaces, Illinois J. Math. 33 (1989), no. 2, 181-209
  6. S. Bloom and G. S. De Souza, Weighted Lipschitz spaces and their analytic characterizations, Constr. Approx, 10 (1994), no. 3, 339-376 https://doi.org/10.1007/BF01212565
  7. B. R. Choe, H. Koo, and H. Yi, Derivatives of Harmonic Bergman and Bloch functions on the ball, J. Math. Anal. Appl. 260 (2001), 100-123 https://doi.org/10.1006/jmaa.2000.7438
  8. K. M. Dyakonov, Equivalent norms on Lipschitz-type spaces of holomorphic functions, Acta. Math. 178 (1997), 143-167 https://doi.org/10.1007/BF02392692
  9. K. M. Dyakonov, Holomorphic functions and quasiconformal mappings with smooth moduli, Adv. Math. 187 (2004), 146-172 https://doi.org/10.1016/j.aim.2003.08.008
  10. K. M. Dyakonov, Strong Hardy-Littlewood theorems for analytic functions and mappings of finite distortion, Math. Z. 249 (2005), no. 3, 597-611 https://doi.org/10.1007/s00209-004-0723-3
  11. H. Hedenrnanlrn, B. Korenblum, and K. Zhu, Theory of Bergman spaces, Springer-Verlag, 2000
  12. M. Pavlovic, On Dyakonov's paper 'Equivalent norms on Lipschitz-type spaces of holomorphic functions', Acta. Math. 183 (1999), 141-143 https://doi.org/10.1007/BF02392949
  13. M. Pavlovic, Introduction to Function Spaces on the Disk, Posebna izdanja 20, Math-ematicki Institut SANU, Beograd 2004
  14. W. Rudin, Function theory in the unit ball of $\mathbb{C}^n$, Springer-Verlag Press, New York, 1980
  15. K. Zhu, VMO, ESV, and Toeplitz operators on the Bergman space, Trans. Amer. Math. Soc. 302 (1987), 617-646 https://doi.org/10.2307/2000860
  16. K. Zhu, Operator Theory in Function Spaces, Marcel Dekker, New York, 1990