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http://dx.doi.org/10.4134/BKMS.2014.51.4.1005

BOUNDED COMPOSITION OPERATORS FROM THE BERGMAN SPACE TO THE HARDY SPACE  

Kasuga, Kazuhiro (Academic Support Center Kogakuin University)
Nakazi, Takahiko (Hokusei Gakuen University)
Publication Information
Bulletin of the Korean Mathematical Society / v.51, no.4, 2014 , pp. 1005-1013 More about this Journal
Abstract
Let ${\phi}$ be an analytic self map of the open unit disc D. In this paper, we study the composition operator $C_{\phi}$ from the Bergman space on D to the Hardy space on D.
Keywords
Bergman space; Hardy space; isometry; bounded composition; Nevanlinna counting function;
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  • Reference
1 T. Nakazi, The Nevanlinna counting functions for Rudin's orthogonal functions, Proc. Amer. Math. Soc. 131 (2003), no. 4, 1267-1271.   DOI   ScienceOn
2 T. Nakazi, Isometric composition operators between two weighted Hardy spaces, Nihonkai Math. J. 17 (2006), no. 2, 111-124.
3 T. Nakazi and T.Watanabe, Properties of a Rudin's orthogonal function which is a linear combination of two inner functions, Sci. Math. Jpn. 57 (2003), no. 2, 413-418.
4 C. Sundberg, Measures induced by analytic functions and a problem of Walter Rudin, J. Amer. Math. Soc. 16 (2003), no. 1, 69-90.   DOI   ScienceOn
5 C. Bishop, Orthogonal functions in $H^{\infty}$, Pacific J. Math. 220 (2005), no. 1, 1-31.   DOI
6 J. Moorhouse and C. Toews, Differences of composition opertors, Contemporary Mathe-matics 321 (2003), 207-213.   DOI
7 W. Smith, Composition operators between Bergman and Hardy spaces, Trans. Amer. Math. Soc. 348 (1996), no. 6, 2331-2348.   DOI   ScienceOn