## $H^1$ boundedness of determinants of vector fields

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- by Loukas Grafakos PDF
- Proc. Amer. Math. Soc.
**125**(1997), 3279-3288 Request permission

## 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 ${\frac {1}{p_{1}}}+\dots +{\frac {1}{p_{l}}}=1$.## References

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## Additional Information

**Loukas Grafakos**- Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211-0001
- MR Author ID: 288678
- ORCID: 0000-0001-7094-9201
- Email: loukas@math.missouri.edu
- 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
- © Copyright 1997 American Mathematical Society
- 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