Abstract
We obtain an asymptotic formula for the norms of composition operators induced by finite Blaschke products on analytic (quotient) Besov spaces in terms of their degree. We also compute the norms of such operators on the true Bloch and Dirichlet spaces.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Allen, R.F., Colonna, F.: On the isometric composition operators on the Bloch space in ℂn. J. Math. Anal. Appl. 355(2), 675–688 (2009)
Arazy, J., Fisher, S.D., Peetre, J.: Möbius invariant function spaces. J. Reine Angew. Math. 363, 110–145 (1985)
Arazy, J., Fisher, S.D., Peetre, J.: Besov Norms of Rational Functions. Lecture Notes Math., vol. 1302, pp. 125–129. Springer, Berlin (1988)
Cowen, C., MacCluer, B.: Composition Operators on Spaces of Analytic Functions. Studies in Advanced Mathematics. CRC Press, Boca Raton (1995)
Garnett, J.B.: Bounded Analytic Functions. Academic Press, San Diego (1981). Reprinted by Springer, New York (2010)
Heins, M.: Some characterizations of finite Blaschke products of positive degree. J. Anal. Math. 46, 162–166 (1986)
Martín, M.J.: Composition operators and geometric function theory (Spanish), 138 pp. Doctoral Thesis, Universidad Autónoma de Madrid (December 2005)
Martín, M.J., Vukotić, D.: Norms and spectral radii of composition operators acting on the Dirichlet space. J. Math. Anal. Appl. 304, 22–32 (2005)
Montes-Rodríguez, A.: The Pick-Schwarz lemma and composition operators on Bloch spaces. Rend. Circ. Mat. Palermo (2) Suppl. 56, 167–170 (1998). International Workshop on Operator Theory (Cefalù, 1997)
Xiong, C.: Norm of composition operators on the Bloch space. Bull. Aust. Math. Soc. 70(2), 293–299 (2004)
Zhu, K.: Analytic Besov spaces. J. Math. Anal. Appl. 157, 318–336 (1991)
Acknowledgements
The authors thankfully acknowledges partial support from MICINN grant MTM2009-14694-C02-01, Spain. The second author was also partially supported by the European ESF Network HCAA (“Harmonic and Complex Analysis and Its Applications”).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media New York
About this chapter
Cite this chapter
Martín, M.J., Vukotić, D. (2013). Norms of Composition Operators Induced by Finite Blaschke Products on Möbius Invariant Spaces. In: Mashreghi, J., Fricain, E. (eds) Blaschke Products and Their Applications. Fields Institute Communications, vol 65. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-5341-3_12
Download citation
DOI: https://doi.org/10.1007/978-1-4614-5341-3_12
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4614-5340-6
Online ISBN: 978-1-4614-5341-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)