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Hardy-type inequalities for vector fields with vanishing tangential components


Authors: Xingfei Xiang and Zhibing Zhang
Journal: Proc. Amer. Math. Soc. 143 (2015), 5369-5379
MSC (2010): Primary 26D10, 42B20, 46E40
DOI: https://doi.org/10.1090/S0002-9939-2015-12668-8
Published electronically: January 23, 2015
MathSciNet review: 3411152
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Abstract: This note studies Hardy-type inequalities for vector fields with the $ L^1$ norm of the operator $ \operatorname {curl}$. In contrast to the well-known results in the whole space for the divergence-free vector fields, we generalize the Hardy-type inequalities to bounded domains and to non-divergence-free vector fields with tangential components vanishing on the boundary.


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Additional Information

Xingfei Xiang
Affiliation: Department of Mathematics, Tongji University, Shanghai 200092, People’s Republic of China
Email: xiangxingfei@126.com

Zhibing Zhang
Affiliation: Department of Mathematics, East China Normal University, Shanghai 200241, People’s Republic of China
Email: zhibingzhang29@126.com

DOI: https://doi.org/10.1090/S0002-9939-2015-12668-8
Keywords: $\operatorname{div}$, $\operatorname{curl}$, Hardy-type inequality, $L^1$ data
Received by editor(s): March 24, 2014
Received by editor(s) in revised form: September 2, 2014, and October 31, 2014
Published electronically: January 23, 2015
Communicated by: Jeremy Tyson
Article copyright: © Copyright 2015 American Mathematical Society

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