DOI QR코드

DOI QR Code

NORM OF THE COMPOSITION OPERATOR FROM BLOCH SPACE TO BERGMAN SPACE

  • Received : 2013.11.07
  • Published : 2014.07.31

Abstract

In this paper, we study some quantity equivalent to the norm of Bloch to $A^p_{\alpha}$ composition operator where Ap $A^p_{\alpha}$ is the weighted Bergman space on the unit ball of $\mathbb{C}^n$ (0 < p < ${\infty}$ and -1 < ${\alpha}$ < ${\infty}$).

Keywords

References

  1. P. Ahern, On the behavior near a torus of functions holomorphic in the ball, Pacific J. Math. 107 (1983), no. 2, 267-278. https://doi.org/10.2140/pjm.1983.107.267
  2. P. Ahern and W. Rudin, Bloch functions, BMO, and boundary zeros, Indiana Univ. Math. J. 36 (1987), no. 1, 131-148. https://doi.org/10.1512/iumj.1987.36.36007
  3. S. Dai, H. Chen, and Y. Pan, The Schwarz-Pick lemma of high order in several variables, Michigan Math. J. 59 (2010), no. 3, 517-533. https://doi.org/10.1307/mmj/1291213955
  4. M. Jevtic, On M-harmonic space $D^s_p$, Filomat 9 (1995), no. 1, 77-82.
  5. E. G. Kwon, Hyperbolic mean growth of bounded holomorphic functions in the ball, Trans. Amer. Math. Soc. 355 (2003), no. 3, 1269-1294. https://doi.org/10.1090/S0002-9947-02-03169-0
  6. E. G. Kwon and J. Lee, Norm of the composition operator mapping Bloch space into Hardy or Bergman space, Commun. Korean Math. Soc. 18 (2003), no. 4, 653-659. https://doi.org/10.4134/CKMS.2003.18.4.653
  7. W. Ramey and D. Ullrich, Bounded mean oscillation of Bloch pull-backs, Math. Ann. 291 (1991), no. 4, 591-606. https://doi.org/10.1007/BF01445229
  8. W. Rudin, Function Theory in the Unit Ball of $\mathbb{C}^n$, Springer-Verlag, New York, 1980.
  9. W. Rudin, Real and Complex Analysis, McGraw-Hill, New York, 1987.
  10. M. Stoll, Invariant Potential Theory in the Unit Ball of $\mathbb{C}^n$, Cambridge Univ. Press, London, 1994.