bmo norm

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The BMO space consists of all the functions having bounded mean oscillation, equipped with the BMO-norm, ?�??. Note that the BMO-norm is not a real norm. We establish an estimate of the BMO-norm of a divergence-free vector field in {\mathbb R}^3 in terms of the operator norm of an associated paracommutator. Moreover, every constant function c satisfies kckBMO = 0. Consequently, functions f and f + c have the same BMO norms whenever c is a constant. In the sequel.
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The same is true for a large class of singular integral transformations cf. Stein, "Harmonic analysis: real variable methods, orthogonality, and oscillatory integrals" , Math. Rubio de Francia, "Weighted norm inequalities and related topics" , Math. Press [a13] N.