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boundedness of determinants of vector fields

Authors:	Loukas Grafakos

Institution:	Department of Mathematics, University of Missouri, Columbia, Missouri 65211-0001

Abstract:	We consider multilinear operators $T(f_{1},\dots , f_{l})$ given by determinants of matrices of the form $(X_{k}f_{j})_{1\le j,k\le l}$ , where the $X_{k}$ 's are $C^{\infty }$ vector fields on $\mathbb {R}^{n}$ . We give conditions on the $X_{k}$ 's so that the corresponding operator maps products of Lebesgue spaces $L^{p_{1}}\times \dots \times L^{p_{l}}$ into some anisotropic space $H^{1}$ , when ${\frac {1}{p_{1}}}+\dots +{\frac {1}{p_{l}}}=1$ .

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