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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

Information

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
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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