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arXiv · 1312.5823

Lorentz space estimates for vector fields with divergence and curl in Hardy spaces

Yoshikazu Giga·Xingfei Xiang
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Abstract

In this note, we establish the estimate on the Lorentz space $L(3/2,1)$ for vector fields in bounded domains under the assumption that the normal or the tangential component of the vector fields on the boundary vanishing. We prove that the $L(3/2,1)$ norm of the vector field can be controlled by the norms of its divergence and curl in the atomic Hardy spaces and the $L^1$ norm of the vector field itself.

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Yoshikazu Giga, Xingfei Xiang. 2013-12-20. Lorentz space estimates for vector fields with divergence and curl in Hardy spaces. https://arxiv.org/abs/1312.5823

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