Compact composition operators on Hardy-Orlicz spaces

Authors

  • Ajay K. Sharma Department of Mathematics, University of Jammu, Jammu-180006, India Author
  • S. D. Sharma Department of Mathematics, University of Jammu, Jammu-180006, India Author

Keywords:

Hardy-Orlicz space, Composition operator, Nevanlinna counting function, vanishing Carleson measure

Subjects:

47B33, 46E38, 30D55

Abstract

In this paper, compact composition operators acting on Hardy-Orlicz spaces HΦ={fınH(D):sup0<r<1ıntDΦ(log+|f(reiθ)|)dσ<ınfty} are studied. In fact, we prove that if Φ is a twice differentiable, non-constant, non-decreasing non-negative, convex function on R, then the composition operator Cφ induced by a holomorphic self-map φ of the unit disk is compact on Hardy-Orlicz spaces HΦ if and only if it is compact on the Hardy space H2.

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Published

2008-07-15