Abstract
The original notion of Carleson measures was introduced in the context of Hardy spaces when L. Carleson solved the corona problem and characterized interpolating sequences for H ∞. This notion has since been generalized to many different contexts, most notably in the context of Bergman spaces in recent decades. Carleson-type measures now play a central role in modern complex analysis, harmonic analysis, and functional analysis.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
A. Aleman, Hilbert spaces of analytic functions between the Hardy space and the Dirichlet space. Proc. Am. Math. Soc. 115, 97–104 (1992)
N. Arcozzi, R. Rochberg, E. Sawyer, Carleson measures for analytic Besov spaces. Rev. Mat. Iberoamericana 18, 443–510 (2002)
A. Aleman, A. Simbotin, Estimates in Möbius invariant spaces of analytic functions. Complex Variables 49, 487–510 (2004)
G. Bao, Z. Lou, R. Qian, H. Wulan, On absolute values of \(\mathcal{Q}_{K}\) functions. Bull. Korean Math. Soc. 53, 561–568 (2016)
L. Carleson, An interpolation problem for bounded analytic functions. Am. J. Math. 80, 921–930 (1958)
L. Carleson, Interpolations by bounded analytic functions and the corona problem. Ann. Math. 76, 547–559 (1962)
P. Duren, Theory of H p Spaces (Academic, New York/London, 1970)
P. Duren, Extension of a theorem of Carleson’s. Bull. Am. Math. 75, 143–146 (1969)
M. Essén, H. Wulan, J. Xiao, Function-theoretic aspects of Möbius invariant \(\mathcal{Q}_{K}\) spaces. J. Funct. Anal. 230, 78–115 (2006)
M. Essén, J. Xiao, Some results on \(\mathcal{Q}_{p}\) spaces, 0 < p < 1. J. Reine Angew. Math. 485, 173–195 (1997)
J. Garnett, Bounded Analytic Functions (Academic, New York, 1982)
H. Hedenmalm, B. Korenblum, K. Zhu, Theory of Bergman Spaces (Springer, New York, 2000)
P. Jones, L ∞ estimates for the \(\bar{\partial }\)-problem in a half plane. Acta Math. 150, 137–152 (1983)
H. Luecking, Forward and reverse Carleson inequalities for functions in Bergman spaces and their derivatives. Am. J. Math. 107, 85–111 (1985)
J. Pau, Bounded Möbius invariant \(\mathcal{Q}_{K}\) spaces. J. Math. Anal. Appl. 338, 1029–1042 (2008)
S. Power, Vanishing Carleson measures. Bull. Lond. Math. Soc. 12, 207–210 (1980)
D. Stegenga, Multipliers of the Dirichlet space. Ill. J. Math. 24, 113–139 (1980)
H. Wulan, J. Zhou, \(\mathcal{Q}_{K}\) and Morrey type spaces. Ann. Acad. Sci. Fenn. Math. 38, 193–207 (2013)
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)
K. Zhu, Operator Theory in Function Spaces, 2nd edn. (American Mathematical Society, Providence, 2007)
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). K-Carleson Measures. In: Mobius Invariant QK Spaces. Springer, Cham. https://doi.org/10.1007/978-3-319-58287-0_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-58287-0_4
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)