Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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COMPACT INTERTWINING RELATIONS FOR COMPOSITION OPERATORS BETWEEN THE WEIGHTED BERGMAN SPACES AND THE WEIGHTED BLOCH SPACES

  • Tong, Ce-Zhong (Department of Mathematics Hebei University of Technology) ;
  • Zhou, Ze-Hua (Department of Mathematics Tianjin University)
  • Received : 2013.01.13
  • Published : 2014.01.01
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Abstract

We study the compact intertwining relations for composition operators, whose intertwining operators are Volterra type operators from the weighted Bergman spaces to the weighted Bloch spaces in the unit disk. As consequences, we find a new connection between the weighted Bergman spaces and little weighted Bloch spaces through this relations.

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References

  1. A. Aleman and J. A. Cima, An integral operator on Hp and Hardy's inequality, J. Anal. Math. 85 (2001), 157-176. https://doi.org/10.1007/BF02788078
  2. A. Aleman and A. G. Siskakis, Integration operators on Bergman spaces, Indiana Univ. Math. J. 46 (1997), no. 2, 337-356.
  3. P. S. Bourdon and J. H. Shapiro, Intertwining relations and extended eigenvalues for analytic Toeplitz operators, Illinois J. Math. 52 (2008), no. 3, 1007-1030.
  4. C. C. Cowen and B. D. MacCluer, Composition Operators on Spaces of Analytic Functions, CRC Press, Boca Raton, 1995.
  5. V. Lomonosov, Invariant subspaces of the family of operators that commute with a completely continuous operator, Funkcional. Anal. i Prilozen 7 (1973), no. 3, 55-56.
  6. S. X. Li, Volterra composition operators between weighted Bergman spaces and Bloch type spaces, J. Korean Math. Soc. 45 (2008), no. 1, 229-248. https://doi.org/10.4134/JKMS.2008.45.1.229
  7. J. H. Shapiro, Composition Operators and Classical Function Theory, Springer Verlag, New York, 1993.
  8. A. G. Siskakis and R. H. Zhao, A Volterra type operator on spaces of analytic functions, Function spaces (Edwardsville, IL, 1998). Contemp. Math., Vol. 232, pp. 299-311, 1999. https://doi.org/10.1090/conm/232/03406
  9. C. Tong and Z. Zhou, Intertwining relations for Volterra operators on the Bergman space, Illinois J. Math., to appear.
  10. J. Xiao, The $Q_p$ carelson measure problem, Adv. Math. 217 (2008), no. 5, 2075-2088. https://doi.org/10.1016/j.aim.2007.08.015
  11. K. H. Zhu, Bloch type spaces of analytic functions, Rocky Mountain J. Math. 23 (1993), no. 3, 1143-1177. https://doi.org/10.1216/rmjm/1181072549
  12. K. H. Zhu, Spaces of Holomorphic Functions in the Unit Ball, Grad. Texts in Math, Springer, 2005.