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On an equivalent class of norms for BMO

Part of: Harmonic analysis in several variables

Published online by Cambridge University Press:  09 April 2009

Yong-Zhuo Chen  and
Ka-Sing Lau
Yong-Zhuo Chen
Affiliation:
Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio 43403, U.S.A.
Ka-Sing Lau
Affiliation:
Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio 43403, U.S.A.
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Abstract

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The BMO norm of f is equivalent to where Pt is the Poisson kernel. In this note, we show that Pt can be replaced by a nonnegative radial function h, which is positive in a neighbourhood of 0, with and , where h is the least decreasing radial majorant of h.

Keywords

BMObounded upper meansequivalent normPoisson kernel.

MSC classification

Secondary: 42B30: $H^p$-spaces 42B99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 46 , Issue 2 , April 1989 , pp. 289 - 295
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Chen, Y. Z. and Lau, K. S., ‘Wiener transformation on functions with bounded means’, submitted.Google Scholar
[2]Chen, Y. Z. and Lau, K. S., ‘Some new classes of Hardy spaces’, J. Funct. Anal., to appear.Google Scholar
[3]Garnett, J. B., Bounded analytic functions (Academic Press, New York, 1981).Google Scholar
[4]Lau, K. S. and Lee, J., ‘On generalized harmonic analysis’, Trans. Amer. Math. Soc. 259 (1980), 75–97.CrossRefGoogle Scholar