On the equivalence of the BMO-norm of divergence-free vector fields and norm of related paracommutators

M. N. Demchenko

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arXiv · 2206.09686

On the equivalence of the BMO-norm of divergence-free vector fields and norm of related paracommutators

M. N. Demchenko

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Abstract

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. The latter is essentially a $\Psi$DO, whose symbol depends linearly on the vector field. Together with the result of P.~Auscher and M.~Taylor concerning the converse estimate, this provides an equivalent norm in the space of divergence-free fields from BMO.

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M. N. Demchenko. 2022-06-20. On the equivalence of the BMO-norm of divergence-free vector fields and norm of related paracommutators. https://arxiv.org/abs/2206.09686

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