Abstract
As a family of Möbius invariant function spaces, \(\mathcal{Q}_{K}\) spaces were first introduced at the beginning of this century. The theory of \(\mathcal{Q}_{K}\) spaces has since attracted considerable attention and experienced rapid development over the past two decades. In this chapter, we define \(\mathcal{Q}_{K}\) spaces, prove several inclusion relations, and construct some important examples of functions in \(\mathcal{Q}_{K}\). Many of the results and techniques here will be needed later on.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
R. Aulaskari, J. Xiao, R. Zhao, On subspaces and subsets of BMOA and UBC. Analysis 15, 101–121 (1995)
M. Essén, H. Wulan, On analytic and meromorphic functions and spaces of \(\mathcal{Q}_{K}\) type. Uppsala Univ. Dep. Math. Rep. 32, 1–26 (2000). Ill. J. Math. 46, 1233–1258 (2002)
M. Essén, H. Wulan, J. Xiao, Function-theoretic aspects of Möbius invariant \(\mathcal{Q}_{K}\) spaces. J. Funct. Anal. 230, 78–115 (2006)
Z. Lou, Composition operators on Bloch type spaces. Analysis (Munich) 23, 81–95 (2003)
S. Li, X. Zhang, S. Xu, The Bergman type operators on the F(p, q, s) type spaces in \(\mathbb{C}^{n}\). Chin. Ann. Math. 38A, (2017) (in Chinese) or Chin. J. Contemp. Math. 38, (2017)
J. Ortega, J. Fábrega, Pointwise multipliers and corona type decomposition in BMOA. Ann. Inst. Fourier (Grenoble) 46, 111–137 (1996)
W. Ramey, D. Ullrich, Bounded mean oscillation of Bloch pull-backs. Math. Ann. 291, 591–606 (1991)
P. Wu, H. Wulan, Characterizations of \(\mathcal{Q}_{T}\) spaces. J. Math. Anal. Appl. 254, 484–497 (2001)
J. Xiao, Holomorphic \(\mathcal{Q}\) Classes. Lecture Notes in Mathematics, vol. 1767 (Springer, Berlin, 2001)
J. Xiao, Geometric \(\mathcal{Q}_{p}\) Functions (Birkhäuser, Basel/Boston/Berlin, 2006)
S. Yamashita, Gap series and α-Bloch functions. Yokohama Math. J. 28, 31–36 (1980)
R. Zhao, Distances from Bloch functions to some Möbius invariant spaces. Ann. Acad. Sci. Fenn. Math. 33, 303–313 (2008)
K. Zhu, Operator Theory in Function Spaces, 2nd edn. (American Mathematical Society, Providence, 2007)
K. Zhu, Bloch type spaces of functions. Rocky Mt. J. Math. 23, 1143–1177 (1993)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Wulan, H., Zhu, K. (2017). \(\mathcal{Q}_{K}\) Spaces. In: Mobius Invariant QK Spaces. Springer, Cham. https://doi.org/10.1007/978-3-319-58287-0_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-58287-0_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-58285-6
Online ISBN: 978-3-319-58287-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)