Log in :: RSS/Atom Feeds
Banach Journal of Mathematical Analysis

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.

Secondary Subjects: 47B38, 47B33, 32A36
Keywords: holomorphic self-map; composition operator; generally weighted Bloch space; $Q^{q}_{\log}$

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers

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
JSTOR: links.jstor.org
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

2009 © Banach Mathematical Research Group