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On an equivalent class of norms for BMO
- Part of
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- Journal:
- Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 46 / Issue 2 / April 1989
- Published online by Cambridge University Press:
- 09 April 2009, pp. 289-295
- Print publication:
- April 1989
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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.
and 
, where 