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$H^{1}$ boundedness of determinants of vector fields


Author: Loukas Grafakos
Journal: Proc. Amer. Math. Soc. 125 (1997), 3279-3288
MSC (1991): Primary 42B30
DOI: https://doi.org/10.1090/S0002-9939-97-03958-0
MathSciNet review: 1403130
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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 $T$ 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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Additional Information

Loukas Grafakos
Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211-0001
Email: loukas@math.missouri.edu

DOI: https://doi.org/10.1090/S0002-9939-97-03958-0
Received by editor(s): December 11, 1995
Received by editor(s) in revised form: May 20, 1996
Additional Notes: Research partially supported by the NSF and the University of Missouri Research Board
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1997 American Mathematical Society

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