Hostname: page-component-76fb5796d-vvkck Total loading time: 0 Render date: 2024-04-26T07:45:38.229Z Has data issue: false hasContentIssue false
  • English
  • Français

NEW CHARACTERIZATIONS OF THE MEROMORPHIC BESOV, Qp AND RELATED CLASSES

Part of: Entire and meromorphic functions, and related topics

Published online by Cambridge University Press:  09 February 2009

R. AULASKARI ,
S. MAKHMUTOV  and
J. RÄTTYÄ
R. AULASKARI*
Affiliation:
Department of Physics and Mathematics, University of Joensuu, PO Box 111, 80101 Joensuu, Finland (email: rauno.aulaskari@joensuu.fi)
S. MAKHMUTOV
Affiliation:
Department of Mathematics and Statistics, Sultan Qaboos University, PO Box 36, Al Khodh 123, Oman Institute of Mathematics, Ufa, 450077, Russia (email: makhm@squ.edu.om)
J. RÄTTYÄ
Affiliation:
Department of Physics and Mathematics, University of Joensuu, PO Box 111, 80101 Joensuu, Finland (email: jouni.rattya@joensuu.fi)
*
✉For correspondence; e-mail: rauno.aulaskari@joensuu.fi
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Functions in the meromorphic Besov, Qp and related classes are characterized in terms of double integrals of certain oscillation quantities involving chordal distances. Some of the results are analogous to the corresponding results in the analytic case.

Keywords

meromorphic functionchordal distancespherical derivativenormal functionQp-classBesov classBergman class

MSC classification

Secondary: 30D45: Bloch functions, normal functions, normal families
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 79 , Issue 1 , February 2009 , pp. 49 - 58
Copyright
Copyright © Australian Mathematical Society 2009

Footnotes

This research was supported in part by the Academy of Finland 121281, IG/SCI/DOMS/07/01, the MEC-Spain MTM2005-07347, and the Spanish Thematic Network MTM2006-26627-E.

References

[1] Aulaskari, R. and Csordas, G., ‘Besov spaces and the Q q,0 classes’, Acta Sci. Math. (Szeged) 60 (1995), 31–48.Google Scholar
[2] Aulaskari, R., Hayman, W. K. and Lappan, P., ‘An integral criterion for automorphic and rotation automorphic functions’, Ann. Acad. Sci. Fenn. 15 (1990), 200–224.Google Scholar
[3] Aulaskari, R. and Lappan, P., ‘Criteria for an analytic function to be Bloch and a harmonic or meromorphic function to be normal’, in: Complex Analysis and Its Applications (Hong Kong, 1993), Pitman Research Notes in Mathematics, 305 (Longman Scientific & Technical, Harlow, 1994), pp. 136–146.Google Scholar
[4] Aulaskari, R., Xiao, J. and Zhao, R., ‘On subspaces and subsets of BMOA and UBC’, Analysis 15 (1995), 101–121.CrossRefGoogle Scholar
[5] Duren, P. and Schuster, A., Bergman Spaces, Mathematical Surveys and Monographs, 100 (American Mathematical Society, Providence, RI, 2004).CrossRefGoogle Scholar
[6] Garnett, J. B., Bounded Analytic Functions, Pure and Applied Mathematics, 96 (Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981).Google Scholar
[7] Haiou, T. and Xiao, J., ‘Two applications of generalized Carleson measures to meromorphic Besov-type spaces’, Kexue Tongbao 43 (1998), 1047–1050 (in Chinese).Google Scholar
[8] Hayman, W. K., ‘The boundary behaviour of Tsuji functions’, Michigan Math. J. 15 (1968), 1–25.CrossRefGoogle Scholar
[9] Hedenmalm, H., Korenblum, B. and Zhu, K., Theory of Bergman Spaces, Graduate Texts in Mathematics, 199 (Springer, New York, 2000).CrossRefGoogle Scholar
[10] Lappan, P., ‘Some results on harmonic normal functions’, Math. Z. 90 (1965), 155–159.CrossRefGoogle Scholar
[11] Lehto, O. and Virtanen, K. I., ‘Boundary behaviour and normal meromorphic functions’, Acta Math. 97 (1957), 47–65.CrossRefGoogle Scholar
[12] Makhmutov, S., ‘Hyperbolic Besov functions and Bloch-to-Besov composition operators’, Hokkaido Math. J. 26 (1997), 699–711.CrossRefGoogle Scholar
[13] Rättyä, J., ‘On some complex function spaces and classes’, Ann. Acad. Sci. Fenn. Math. Diss. 124 (2001), 1–73.Google Scholar
[14] Rättyä, J., ‘n-th derivative characterisations, mean growth of derivatives and F(p,q,s)’, Bull. Aust. Math. Soc. 68(3) (2003), 405–421.CrossRefGoogle Scholar
[15] Stroethoff, K., ‘The Bloch space and Besov spaces of analytic functions’, Bull. Aust. Math. Soc. 54 (1996), 211–219.CrossRefGoogle Scholar
[16] Wulan, H., ‘On some classes of meromorphic functions’, Ann. Acad. Sci. Fenn. Diss. 116 (1998), 1–57.Google Scholar
[17] Zhu, K., ‘Analytic Besov functions’, J. Math. Anal. Appl. 157 (1991), 318–336.CrossRefGoogle Scholar