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| In this paper, we prove that, for every $bin BMO(R^{n})$ and $finH^{1}(R^{n})$, by use of a kind of compensated quantities, we canget a decomposition of the product space $BMO(R^{n}) imesH^{1}(R^{n})$. Precisely, we obtain, for $fin H^{1}(R^{n})$, $binBMO(R^{n})$, the point-wise product $bcdot f$ as a Schwartzdistribution, denoted by $b imes fin S'(R^{n})$, can be decomposedinto two parts associated with the bilinear operators, that is$b imes f=u+v$, where $uin L^{1}(R^{n})$ and $v$ belongs to theHardy-Orlicz space $H^{mathcal{P}}(R^{n})$. |
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| Keywords:Commutator, Compactness, $VMO$, Schr"{o}dinger operator,Riesz transform. |
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