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Composition operators on weighted Bergman-Orlicz spaces

  • Ajay K. Sharma (a1) and S. D. Sharma (a2)

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In this paper, composition operators acting on Bergman-Orlicz spaces

are studied, where ψ is a non-constant, non-decreasing convex function defined on (-∞, ∞) which satisfies the growth condition . In fact, under a mild condition on ∞, we show that every holomorphic-self map ∞ of induces a bounded composition operator on and C is compact on if and only if it is compact on .

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References

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[1]Axler, S., ‘Bergman spaces and their operators’, in Surveys of some recent results in operator theory, Vol. 1, Pitman Research Notes in Math. 171 (Longman Science and Technology, Harlow, 1988), pp. 150.
[2]Cima, J. and Matheson, A., ‘Essential norms of a Composition operators and Aleksandrov Measures’, Pacific J. Math. 179 (1997), 5963.
[3]Hasumi, M. and Kataoka, S., ‘Remarks on Hardy–Orlicz classes’, Arch. Math. 51 (1988), 455463.
[4]MacCluer, B.D. and Shapiro, J.H., ‘Angular derivatives and compact composition operators on Hardy and Bergman spaces’, Canad. J. Math. 38 (1986), 878906.
[5]Schwartz, H.J., Composition operators on HP, (Thesis) (University of Toledo, 1969).
[6]Shapiro, J.H. and Sundberg, C., ‘Compact composition operators on L 1’, Proc. Amer. Math. Soc. 108 (1990), 443449.
[7]Shapiro, J.H. and Taylor, P.D., ‘Compact, nuclear and Hilbert-Schmidt composition operators on H 2’, Indiana Univ. Math. J. 23 (1973), 471496.
[8]Shapiro, J.H., ‘The essential norm of a composition operator’, Ann. of Math. (2) 125 (1987), 375404.
[9]Shapiro, J.H., Composition operators and classical function theory (Springer-Verlag, New York, 1993).
[10]Stevic, S., ‘On generalised weighted Bergman spaces’, Complex Var. Theory. Appl. 49 (2004), 109124.
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Composition operators on weighted Bergman-Orlicz spaces

  • Ajay K. Sharma (a1) and S. D. Sharma (a2)

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