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Note on the Space Bmoa

Published online by Cambridge University Press:  20 November 2018

Jun Soo Choa
Jun Soo Choa*
Affiliation:
Department of Mathematics Education Sung Kyun Kwan University Jongro-gu, Seoul 110-745 Korea
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Abstract

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Let D be the unit disc in the complex plane. It is shown that

(i) for 0 < p < 2, there exists an analytic function f ∊ BMOA for which

and

(ii) for 2 < p < ∞, there exists an analytic function f ∉ BMOA for which

This settles the question of Stroethoff [5] on BMOA.

Keywords

30D55.Bloch spacebounded mean oscillation
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 35 , Issue 1 , 01 March 1992 , pp. 40 - 45
Copyright
Copyright © Canadian Mathematical Society 1992

References

1. Baernstein, A., Analytic Functions of Bounded Mean Oscillation. In: Aspects of Contemporary Complex Analysis, Academic Press, New York, 3–36.Google Scholar
2. Garnett, J. B., Bounded Analytic Functions, Academic Press, New York, 1981.Google Scholar
3. Hallenbeck, D. J. and Samotij, K., On radial variation of bounded analytic functions, Complex Variables, 15(1990),43–52.Google Scholar
4. Kennedy, P. B., On the derivative of a function of bounded characteristic, Quart. J. Math. Oxford, 15(1964),337–341.Google Scholar
5. Stroethoff, K., Besov-type characterization for the Bloch space, Bull. Austral. Math. Soc, 39(1989),405–420.Google Scholar