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n-th derivative characterisations, mean growth of derivatives and F(p, q, s)

Published online by Cambridge University Press:  17 April 2009

J. Rättyä
J. Rättyä
Affiliation:
Department of Mathematics, University of Joensuu, P. O. Box 111, FIN-80101 Joensuu, Finland, e-mail: rattya@cc.joensuu.fi
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Abstract

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Various n-th derivative characterisations involving different kinds of oscillations of F(p,q,s) functions are established, and the mean growth of derivatives of F(p,q,s) functions is considered. Moreover, inclusion relations between certain analytic function spaces are discussed.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 68 , Issue 3 , December 2003 , pp. 405 - 421
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Aulaskari, R., Girela, D. and Wulan, H., ‘Taylor coefficients and mean growth of the derivative of Qp functions’, J. Math. Anal. Appl. 258 (2001), 415–428.CrossRefGoogle Scholar
[2]Aulaskari, R., Nowak, M. and Zhao, R., ‘The n-th derivative characterization of Möbius invariant Dirichlet space’, Bull. Austral. Math. Soc. 58 (1998), 43–56.CrossRefGoogle Scholar
[3]Danikas, N., ‘Some Banach spaces of analytic functions’, in Function spaces and complex analysis (Joensuu, 1997), Univ. Joensuu Dept. Math. Rep. Ser. 2 (University of Joensuu, Joensuu, 1999), pp. 9–35.Google Scholar
[4]Duren, P., Theory of Hp spaces (Academic Press, New York and London, 1970).Google Scholar
[5]Fàbrega, J. and Ortega, J.M., ‘Pointwise multipliers and corona type decomposition in BMOA’, Ann. Inst. Fourier. (Grenoble) 46 (1996), 111–137.Google Scholar
[6]Flett, T.M., ‘The dual of an inequality of Hardy and Littlewood and some related inequalitites’, J. Math. Anal. Appl. 38 (1972), 746–765.CrossRefGoogle Scholar
[7]Garnett, J., Bounded analytic functions, Pure and Applied Mathematics 96 (Academic Press, 1981).Google Scholar
[8]Heittokangas, J., ‘On complex differential equations in the unit disc’, Ann. Acad. Sci. Fenn. Math. Dissertationes 122 (2000), 1–54.Google Scholar
[9]Mateljević, M. and Pavlović, M., ‘Lp-behaviour of power series with positive coefficients and Hardy spaces’, Proc. Amer. Math. Soc. 87 (1983), 309–316.Google Scholar
[10]Rättyä, J., ‘On some complex function spaces and classes’, Ann. Acad. Sci. Fenn. Math. Dissertationes 124 (2001), 1–73.Google Scholar
[11]Stroethoff, K., ‘Besov-type characterizations for the Bloch space’, Bull. Austral. Math. Soc. 39 (1989), 405–420.CrossRefGoogle Scholar
[12]Stroethoff, K., ‘The Bloch space and Besov spaces of analytic functions’, Bull. Austral. Math. Soc. 54 (1996), 211–219.CrossRefGoogle Scholar
[13]Zhao, R., ‘On a general family of function spaces’, Ann. Acad. Sci. Fenn. Dissertationes 105 (1996), 1–56.Google Scholar
[14]Yoneda, R., ‘Characterizations of Bloch space and Besov spaces by oscillations’, Hokkaido Math. J. 29 (2000), 409–451.CrossRefGoogle Scholar
[15]Zhu, K., Operator theory in function spaces, Monographs and Testbooks in Pure and Applied Mathematics 139 (Marcel Dekker, New York, 1990).Google Scholar
[16]Zygmund, A., Trigonometric series (Cambridge Univ. Press, London, 1959).Google Scholar