Sharp convex Lorentz-Sobolev inequalities
Sharp convex Lorentz-Sobolev inequalities
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DOI：
10.1007/s00208-010-0555-x
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发表时间：
2011-05-01
影响因子：
1.4
通讯作者：
Zhang, Gaoyong
中科院分区：
文献类型：
--
作者：
Ludwig, Monika;Xiao, Jie;Zhang, Gaoyong
通过L（p）Minkowski问题，将Lorentz积分的水平集凸化，得到了新的尖锐的Lorentz-Sobolev不等式.对Lipschitz星星体证明了新的L（p）等容不等式和等周不等式.证明了锐凸Lorentz-Sobolev不等式是等容不等式和等周不等式的解析类似。
New sharp Lorentz-Sobolev inequalities are obtained by convexifying level sets in Lorentz integrals via the L (p) Minkowski problem. New L (p) isocapacitary and isoperimetric inequalities are proved for Lipschitz star bodies. It is shown that the sharp convex Lorentz-Sobolev inequalities are analytic analogues of isocapacitary and isoperimetric inequalities.