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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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$H^1$ 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 ${\frac {1}{p_{1}}}+\dots +{\frac {1}{p_{l}}}=1$.
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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