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XXXIII: 16, 342-348, LNM 1709 (1999)
GRANDITS, Peter
Some remarks on L$^\infty$, H$^\infty$, and $BMO$ (Martingale theory)
It is known from 1212 that neither $L^\infty$ nor $H^\infty$ is dense in $BMO$. This article answers a question raised by Durrett (Brownian Motion and Martingales in Analysis, Wadworth 1984): Does there exist a $BMO$-martingale which has a best approximation in $L^\infty$? The answer is negative, but becomes positive if $L^\infty$ is replaced with $H^\infty$
Keywords: $BMO$, Hardy spaces
Nature: Original
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