Journal d'Analyse Mathématique

, Volume 87, Issue 1, pp 433–450 | Cite as

Composition operators on a local Dirichlet space

  • Donald Sarason
  • Jorge-Nuno O. Silva


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    A. Aleman,Hilbert spaces of analytic functions between the Hardy and the Dirichlet space, Proc. Amer. Math. Soc.115 (1992), 97–104.MathSciNetCrossRefGoogle Scholar
  2. [2]
    J. B. Gamett,Bounded Analytic Functions, Academic Press, New York, 1981.Google Scholar
  3. [3]
    D. Luecking,A technique for characterizing Carleson measures on Bergman spaces, Proc. Amer. Math. Soc.87 (1983), 656–660.MathSciNetCrossRefGoogle Scholar
  4. [4]
    B. D. MacCluer and J. H. Shapiro,Angular derivatives and compact composition operators on the Hardy and Bergman spaces, Canad. J. Math.38 (1986), 878–906.MathSciNetCrossRefGoogle Scholar
  5. [5]
    Z. Nehari,Conformai Mapping, McGraw-Hill, New York, 1952.MATHGoogle Scholar
  6. [6]
    R. Nevanlinna,Remarques sur le lemme de Schwarz, C. R. Acad. Sci. Paris188 (1929), 1027–1029.MATHGoogle Scholar
  7. [7]
    S. Richter,A representation theorem for cyclic analytic two-isometries. Trans. Amer. Math. Soc. 328(1991), 326–349.MathSciNetCrossRefGoogle Scholar
  8. [8]
    S. Richter and C. Sundberg,A formula for the local Dirichlet integral. Michigan Math. J.38 (1991), 355–379.MathSciNetCrossRefGoogle Scholar
  9. [9]
    D. Sarason,Sub-Hardy Hilbert Spaces in the Unit Disk, Wiley, New York, 1994.MATHGoogle Scholar
  10. [10]
    D. Sarason,Local Dirichlet spaces as de Branges-Rovnyak spaces, Proc. Amer. Math. Soc.125 (1997), 2133–2139.MathSciNetCrossRefGoogle Scholar
  11. [11]
    J. H. Shapiro,The essential norm of a composition operator, Ann. of Math.125 (1987), 375–404.MathSciNetCrossRefGoogle Scholar
  12. [12]
    J. H. Shapiro,Composition Operators and Classical Function Theory, Springer-Verlag, New York, 1993.CrossRefGoogle Scholar
  13. [13]
    N. Zorboska,Composition operators on weighted Dirichlet spaces, Proc. Amer. Math. Soc.126 (1998), 2013–2023.MathSciNetCrossRefGoogle Scholar

Copyright information

© Hebrew University of Jerusalem 2002

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of California BerkeleyCAUSA
  2. 2.Departamento de MatemáticaUniversidade de LisboaLisboaPortugal

Personalised recommendations