151
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

A brief note on compactness of composition operators on H2

&
Pages 68-77 | Received 08 Mar 2017, Accepted 06 Dec 2017, Published online: 22 Dec 2017

References

  • Duren PL . Theory of Hp spaces. New York (NY): Academic Press; 1970.
  • Garnett JB . Bounded analytic functions. New York (NY): Academic Press; 1982.
  • Koosis P . Introduction to Hp spaces. 2nd ed. Cambridge: Cambridge University Press; 1998.
  • Shapiro JH . Composition operators and classical function theory. New York (NY): Springer-Verlag; 1993.
  • Shapiro JH . The essential norm of a composition operator. Ann Math. 1987;125(2):375–404.
  • Carroll T , Cowen CC . Compact composition operators not in the Schatten classes. J Oper Theor. 1991;26(1):109–120.
  • Cowen CC , MacCluer BD . Composition operators on spaces of analytic functions. Boca Raton (FL): CRC Press; 1995.
  • Luecking D , Zhu K . Composition operators belonging to the Schatten ideals. Amer J Math. 1992;114(5):1127–1145.
  • Lefèvre P , Li D , Queffélec H , et al . Some examples of compact composition operators on H2 . J Funct Anal. 2008;255(11):3098–3124.
  • Zhu Y . Geometric properties of composition operators belonging to Schatten classes. Int J Math Math Sci. 2001;26(4):239–248.
  • Jones M . Compact composition operators not in the Schatten classes. Proc Amer Math Soc. 2006;134(7):1947–1953.
  • Akeroyd JR . On Shapiro’s compactness criterion for composition operators. J Math Anal Appl. 2011;379(1):1–7.
  • Li D , Queffélec H , Rodriguez-Piazza L . On approximation numbers of composition operators. J Approx Theory. 2012;164(4):431–459.
  • Queffélec H , Seip K . Decay rates for approximation numbers of composition operators. J Anal Math. 2015;125(1):371–399.
  • Tsuji M . Potential theory in modern function theory. New York (NY): Chelsea; 1975.
  • El-Fallah O , Kellay K , Shabankhah M , et al . Level sets and composition operators on the Dirichlet space. J Funct Anal. 2011;260:1721–1733.
  • Wulan H , Zheng D , Zhu K . Compact composition operators on BMOA and the Bloch space. Proc Amer Math Soc. 2009;137(11):3861–3868.
  • Schwartz JH . Composition operators on Hp [Thesis]. University of Toledo; 1969.
  • Shapiro JH , Taylor PD . Compact, nuclear, and Hilbert-Schmidt composition operators on H2 . Indiana Univ Math J. 1973;23:471–496.
  • Dolzhenko EP , Kolesnikov SV . The behavior of conformal maps of domains near convex boundary arcs. Math Notes. 2011;90(3–4):485–497. Russian. Translated from: Mat Zametki 2011 ;90(4):501--516.
  • Royden HL . Real analysis. 3rd ed. Upper Saddle River, NJ: Prentice Hall; 1988.
  • El-Fallah O , El Ibbaoui M , Naqos H . Composition operators with univalent symbol in Schatten classes. J Funct Anal. 2014;266(3):1547–1564.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.