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Composition Operators Induced by Analytic Maps to the Polydisk

Published online by Cambridge University Press:  20 November 2018

Kei Ji Izuchi ,
Quang Dieu Nguyen  and
Shûichi Ohno
Kei Ji Izuchi
Affiliation:
Department of Mathematics, Niigata University, Niigata 950-2181, Japan email: izuchi@m.sc.niigata-u.ac.jp
Quang Dieu Nguyen
Affiliation:
Department of Mathematics, Hanoi University of Education (Dai Hoc Pham Hanoi), Hanoi, Vietnam email: dieu vn@yahoo.com
Shûichi Ohno
Affiliation:
Nippon Institute of Technology, Miyashiro, Minami-Saitama 345-8501, Japan email: ohno@nit.ac.jp
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Abstract

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We study properties of composition operators induced by symbols acting from the unit disk to the polydisk. This result will be involved in the investigation of weighted composition operators on the Hardy space on the unit disk and, moreover, be concerned with composition operators acting from the Bergman space to the Hardy space on the unit disk.

Keywords

47B3332A3530H10composition operatorsHardy spacespolydisk
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 64 , Issue 6 , 01 December 2012 , pp. 1329 - 1340
Copyright
Copyright © Canadian Mathematical Society 2012

References

[1] Cowen, C. C. and Mac Cluer, B. D., Composition operators on spaces of analytic functions. Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1995.Google Scholar
[2] Garnett, J. B., Bounded analytic functions. Revised First Ed., Graduate Texts in Mathematics, 236, Springer, New York, 2007.Google Scholar
[3] Izuchi, K. and Yang, R., Strictly contractive compression on backward shift invariant subspaces over the torus. Acta Sci. Math. (Szeged) 70(2004), no. 1–2, 147–165.Google Scholar
[4] Koo, H. and Smith, W., Composition operators between Bergman spaces of functions of several variables. In: Recent advances in operator-related function theory, Contemp. Math. 393, American Mathematical Society, Providence, RI, 2006, pp. 123–131.Google Scholar
[5] Rudin, W., Function theory in polydiscs. W. A. Benjamin, New York-Amsterdam, 1969.Google Scholar
[6] Shapiro, J. H., Composition operators and classical function theory. Universitext: Tracts in Mathematics, Springer-Verlag, New York, 1993.Google Scholar
[7] Smith, W., Composition operators between Bergman and Hardy spaces. Trans. Amer. Math. Soc. 348(1996), no. 6, 2331–2348. http://dx.doi.org/10.1090/S0002-9947-96-01647-9 Google Scholar
[8] Stessin, M. and Zhu, K., Composition operators induced by symbols defined on a polydisk. J. Math Anal. Appl. 319(2006), no. 2, 815–829. http://dx.doi.org/10.1016/j.jmaa.2005.06.041 Google Scholar
[9] Thomas, P. J., Sampling sets for Hardy spaces of the disk. Proc. Amer. Math. Soc. 126(1998), no. 10, 2927–2932. http://dx.doi.org/10.1090/S0002-9939-98-04411-6 Google Scholar
[10] Zhu, K., Operator theory on function spaces. Second Ed., Mathematical Surveys and Monographs, 138, American Mathematical Society, Providence, RI, 2007.Google Scholar