### Composition operators between generally weighted Bloch spaces and $Q_{log}^q$ space

Haiying Li and Peide Liu
Source: Banach J. Math. Anal. Volume 3, Number 1 (2009), 99-110.

#### Abstract

Let $\varphi$ be a holomorphic self-map of the open unit disk $D$ on the complex plane and $p,\ q>0.$ In this paper, the boundedness and compactness of composition operator $C_{\varphi}$ from generally weighted Bloch space $B^{p}_{\log}$ to $Q^{q}_{\log}$ are investigated.

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Secondary Subjects: 47B38, 47B33, 32A36
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Permanent link to this document: http://projecteuclid.org/euclid.bjma/1240336427
Mathematical Reviews number (MathSciNet): MR2461750
Zentralblatt MATH identifier: 1163.47019

### References

K.R.M. Attele, Toeplitz and Hankel on Bergman one space , Hokaido, Math. J., 21 (1992), 279–293.
Mathematical Reviews (MathSciNet): MR1169795
Zentralblatt MATH: 0789.47021
R. Aulaskari, J. Xiao and R. Zhao, On subspaces and subsets of BMOA and UBC, Analysis, 15 (1995), 101–121.
Mathematical Reviews (MathSciNet): MR1344246
J. Cima and D. Stegenda, Hankel operators on $H^p$, in: Earl R. Berkson, N. T. Peck, J. Ulh(Eds.), Analysis at urbana 1, in: London Math. Soc. Lecture Note ser., Cambridge Univ. Press, Cambridge, 137 (1989), 133–150.
Mathematical Reviews (MathSciNet): MR1009172
C.C. Cowen and B.D. MacCluer, Composition operators on spaces of analytic functions, CRC Press, Boca Roton, 1995.
Mathematical Reviews (MathSciNet): MR1397026
P. Galanopoulos, On $B_\log$ to $Q_\log^p$ pullbacks, J. Math. Anal. Appl., 337(1) (2008), 712–725.
Mathematical Reviews (MathSciNet): MR2356105
Digital Object Identifier: doi:10.1016/j.jmaa.2007.02.049
Zentralblatt MATH: 1137.30015
H. Li, P. Liu and M. Wang, Composition operators between generally weighted Bloch spaces of polydisk, J. Inequal. Pure Appl. Math., 8(3) (2007), Article85, 1–8.
Mathematical Reviews (MathSciNet): MR2345940
K. Madigan and A. Matheson, Compact composition operators on the Bloch space, Trans. Amer. Math. Soc., 347 (1995), 2679–2687.
Mathematical Reviews (MathSciNet): MR1273508
Digital Object Identifier: doi:10.2307/2154848
Zentralblatt MATH: 0826.47023
W. Ramey and D. Ulrich, Bounded mean oscillation of Bloch pull-backs, Math. Ann., 291 (1991), 591–606.
Mathematical Reviews (MathSciNet): MR1135533
Digital Object Identifier: doi:10.1007/BF01445229
Zentralblatt MATH: 0727.32002
A. Siskakis and R. Zhao, A Volterra type operator on spaces on spaces of analytic functions, in: Contemp. Math., 232 (1999), 299–311.
Mathematical Reviews (MathSciNet): MR1678342
Zentralblatt MATH: 0955.47029
J. Xiao, The $Q_p$ corona theorem, Pacific J. Math., 194 (2000), 491–509.
Mathematical Reviews (MathSciNet): MR1760796
Zentralblatt MATH: 1041.46020
J. Xiao, Holomorphic $Q$ Classes, Lecture Notes in Math., Springer, >b<1767>/<, 2001.
Mathematical Reviews (MathSciNet): MR1869752
Zentralblatt MATH: 0983.30001
J. Xiao, Geometric $Q_p$ functions, Front. Math., Birkh$\ddota$user, 2006.
Mathematical Reviews (MathSciNet): MR2257688
Zentralblatt MATH: 1104.30036
R. Yoneda, The composition operators on the weighted Bloch space, Arch. Math., 78 ( 2002), 310–317.
Mathematical Reviews (MathSciNet): MR1895504
Digital Object Identifier: doi:10.1007/s00013-002-8252-y
Zentralblatt MATH: 1038.47020
R. Zhao, On logarithmic Carleson measures, Acta Sci. Math.(Szeged), 69(3-4) (2003), 605–618.
Mathematical Reviews (MathSciNet): MR2034196
Kehe Zhu, Operator Theory on Function Spaces, New York, 1990.
Kehe Zhu, Spaces of Holomorphic functions in the unit ball, New York, 2005.
Mathematical Reviews (MathSciNet): MR2115155

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