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2000 | 139 | 3 | 245-260
Tytuł artykułu

Composition operators: $N_α$ to the Bloch space to $Q_β$

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Let $N_α$,B and Q_β be the weighted Nevanlinna space, the Bloch space and the Q space, respectively. Note that B and $Q_β$ are Möbius invariant, but $N_α$ is not. We characterize, in function-theoretic terms, when the composition operator $C_ϕ f=f◦ϕ$ induced by an analytic self-map ϕ of the unit disk defines an operator $C_ϕ:N_α→B$, $B→Q_β$, $N_α→Q_β$ which is bounded resp. compact.
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autor
  • Institute of Analysis, TU-Braunschweig PK 14(Forum) D-38106 Braunschweig, Germany, xiao@badbit.math2.nat.tu-bs.de
  • School of Mathematical Sciences, Peking University, Beijing 100871, China
Bibliografia
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  • [ANZ] R. Aulaskari, M. Norwak and R. Zhao, The n-the derivative characterizations of Möbius invariant Dirichlet spaces, Bull. Austral. Math. Soc. 58 (1998), 43-56.
  • [ASX] R. Aulaskari, D. Stegenga and J. Xiao, Some subclasses of BMOA and their characterization in terms of Carleson measures, Rocky Mountain J. Math. 26 (1996), 485-506.
  • [AXZ] R. Aulaskari, J. Xiao and R. Zhao, On subspaces and subclasses of BMOA and UBC, Analysis 15 (1995), 101-121.
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  • [BCM] P. S. Bourdon, J. A. Cima and A. L. Matheson, Compact composition operators on BMOA, Trans. Amer. Math. Soc. 351 (1999), 2183-2196.
  • [EX] M. Essén and J. Xiao, Some results on $Q_p$ spaces, 0 < p < 1, J. Reine Angew. Math. 485 (1997), 173-195.
  • [J] H. Jarchow, Locally Convex Spaces, Teubner, 1981.
  • [JX] H. Jarchow and J. Xiao, Composition operators between Nevanlinna classes and Bergman spaces with weights, J. Operator Theory, to appear.
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  • [MM] K. Madigan and A. Matheson, Compact composition operators on the Bloch space, Trans. Amer. Math. Soc. 347 (1995), 2679-2687.
  • [NX] A. Nicolau and J. Xiao, Bounded functions in Möbius invariant Dirichlet spaces, J. Funct. Anal. 150 (1997), 383-425.
  • [RU] W. Ramey and D. Ullrich, Bounded mean oscillation of Bloch pull-backs, Math. Ann. 291 (1991), 591-606.
  • [SS] J. H. Shapiro and A. L. Shields, Unusual topological properties of the Nevanlinna Class, Amer. J. Math. 97 (1976), 915-936.
  • [ST] J. H. Shapiro and P. D. Taylor, Compact, nuclear, and Hilbert-Schmidt composition operators on $H^2$, Indiana Univ. Math. J. 23 (1973), 471-496.
  • [SZ] W. Smith and R. Zhao, Composition operators mapping into the $Q_p$ spaces, Analysis 17 (1997), 239-263.
  • [Str] K. Stroethoff, Nevanlinna-type characterizations for the Bloch space and related spaces, Proc. Edinburgh Math. Soc. 33 (1990), 123-142.
  • [T] M. Tjani, Compact composition operators on some Möbius invariant Banach spaces, Ph.D. Thesis, Michigan State Univ. 1996.
  • [X1] J. Xiao, Carleson measure, atomic decomposition and free interpolation from Bloch space, Ann. Acad. Sci. Fenn. Ser. A.I. Math. 19 (1994), 35-44.
  • [X2] J. Xiao, Compact composition operators on the area-Nevanlinna class, Exposition. Math. 17 (1999), 255-264.
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Bibliografia
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bwmeta1.element.bwnjournal-article-smv139i3p245bwm
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