2024-03-29T10:00:48Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/698482022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116LORENTZ SPACE ESTIMATES FOR VECTOR FIELDS WITH DIVERGENCE AND CURL IN HARDY SPACESGIGA, YOSHIKAZUXIANG, XINGFEIopen accessLorentz space estimatedivergencecurlHardy spaces.410In this note, we establish the estimate on the Lorentz space L(3=2; 1) for vector elds in bounded domains under the assumption that the normal or the tangential component of the vector elds on the boundary vanishing. We prove that the L(3=2; 1) norm of the vector eld can be controlled by the norms of its divergence and curl in the atomic Hardy spaces and the L1 norm of the vector eld itself.Department of Mathematics, Hokkaido University2013-10-30engdepartmental bulletin paperVoRhttps://doi.org/10.14943/84188http://hdl.handle.net/2115/6984810.14943/84188Hokkaido University Preprint Series in Mathematics1044111https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69848/1/pre1044.pdfapplication/pdf325.88 KB2013-10-30