Optimal Sobolev norms in the affine class

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• 作者：Qingzhong Huang^a ; ^{hqz376560571@163.com" class="auth_mail" title="E-mail the corresponding author} ; Ai-Jun Li^b ; ^{liaijun72@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：LpLp surface isotropic position ; Functional LpLp surface isotropic position ; LpLp affine energy ; LpLp sine energy ; (p ; 2)(p ; 2) Fisher information matrix
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：1 April 2016
• 年：2016
• 卷：436
• 期：1
• 页码：568-585
• 全文大小：406 K

文摘

Optimal Sobolev norms under volume preserving affine transformations are considered. It turns out that this minimal transform is equivalent to the b=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X15011361&_mathId=si1.gif&_user=111111111&_pii=S0022247X15011361&_rdoc=1&_issn=0022247X&md5=6cf52860b3efb0de0da88f23529c7858" title="Click to view the MathML source">(p,2)$(p,2)$ Fisher information matrix defined by Lutwak, Lv, Yang, and Zhang. Furthermore, some analytic inequalities regarding to the b=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X15011361&_mathId=si124.gif&_user=111111111&_pii=S0022247X15011361&_rdoc=1&_issn=0022247X&md5=446fbea69d1f28221829a7ad3d295008" title="Click to view the MathML source">L^p$L^p$ affine and b=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X15011361&_mathId=si124.gif&_user=111111111&_pii=S0022247X15011361&_rdoc=1&_issn=0022247X&md5=446fbea69d1f28221829a7ad3d295008" title="Click to view the MathML source">L^p$L^p$ sine energies for the optimal function are investigated.