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Decomposition of BMO functions on normal Lie groups. (Chinese) Zbl 0682.43008

The aim of this paper is to generalize a theorem of C. Fefferman and E. M. Stein in harmonic analysis concerning the decomposition of BMO functions on \(R^ n\), the so-called Fefferman-Stein decomposition, to those on the normal Lie groups which mean the connected Lie groups having bi-invariant metric. The main result is as follows: Let G be a normal Lie group, then for any \(f\in BMO(G)\), there exist \(\{\phi_ j\}\), \(j=0,1,...,n\) belonging to \(L^{\infty}(G)\), such that \[ f=\phi_ 0+\sum^{n}_{j=1}R_ j(\phi_ j)+const.\quad and\quad C_ n^{- 1}\| f\|_{BMO}\leq \sum^{n}_{j=0}\| \phi_ j\|_{\infty}\leq C_ n\| f\|_{BMO} \] where n is dimension of the group manifold G, \(C_ n\) is a constant depending only on n, and \(R_ j\) is the j-th Riesz transform accordingly defined.
Reviewer: J.Na

MSC:

43A80 Analysis on other specific Lie groups
22E30 Analysis on real and complex Lie groups
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