J. Aust. Math. Soc.  76 (2004), 189-206
Composition operators in Orlicz spaces

Yunan Cui
  Department of Mathematics
  Harbin University of Sciences and Technology
  52 Xuefu Road, Nanang. Dist.
  Harbin, Heilongjiang 150080 P. R. of China
  cuiya@mail.hrbust.edu.cn
Henryk Hudzik
  Faculty of Mathematics
  and Computer Science
  Adam Mickiewicz University
  Umultowska 87
  61-614 Poznan
  Poland
  hudzik@amu.edu.pl
Romesh Kumar
  Department of Mathematics
  University of Jammu
  Jammu-180 004
  India
  romesh_jammu@yahoo.com
and
Lech Maligranda
  Department of Mathematics
  Lulea University of Technology
  SE-97187 Lulea
  Sweden
  lech@sm.luth.se


Abstract
Composition operators $C_{\tau}$ between Orlicz spaces $L^{\varphi}(\Omega,\Sigma,\mu)$ generated by measurable and nonsingular transformations $\tau$ from $\Omega$ into itself are considered. We characterize boundedness and compactness of the composition operator between Orlicz spaces in terms of properties of the mapping $\tau$, the function $\varphi$ and the measure space $(\Omega,\Sigma,\mu)$. These results generalize earlier results known for $L^p$-spaces.
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