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

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Published: Jun 30, 2016
DOI: https://doi.org/10.5556/j.tkjm.47.2016.1932
Keywords:
Lorentz space estimate divergence curl Hardy spaces

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Yoshikazu Giga
Xingfei Xiang

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 vanishes. 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.

Article Details

How to Cite
Giga, Y., & Xiang, X. (2016). Lorentz space estimates for vector fields with divergence and curl in Hardy spaces. Tamkang Journal of Mathematics, 47(2), 249–260. https://doi.org/10.5556/j.tkjm.47.2016.1932
Issue
Vol. 47 No. 2 (2016)
Section
Papers
Author Biographies

Yoshikazu Giga

Graduate School of Mathematical Sciences, University of Tokyo, Tokyo 153-8914, Japan.

Xingfei Xiang

Department ofMathematics, Tongji University, Shanghai 200092, P. R. China.

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