Sharp affine Sobolev type inequalities via the L_p Busemann-Petty centroid inequality

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• 作者：J. Haddad^a ; ^{julianhaddad@ufmg.br" class="auth_mail" title="E-mail the corresponding author} ; C.H. Jimé ; nez^b ; ^{hugojimenez@mat.puc-rio.br" class="auth_mail" title="E-mail the corresponding author} ; M. Montenegro^a ; ^{montene@mat.ufmg.br" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 46E35 ; secondary ; 51M16
• 刊名：Journal of Functional Analysis
• 出版年：2016
• 出版时间：15 July 2016
• 年：2016
• 卷：271
• 期：2
• 页码：454-473
• 全文大小：386 K

文摘

We show that the L_p$L_p$ Busemann–Petty centroid inequality provides an elementary and powerful tool to the study of some sharp affine functional inequalities with a geometric content, like log-Sobolev, Sobolev and Gagliardo–Nirenberg inequalities. Our approach allows also to characterize directly the corresponding equality cases.