In between the inequalities of Sobolev and Hardy

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• 作者：Juha Lehrbä ; ck^a ; ^{juha.lehrback@jyu.fi" class="auth_mail" title="E-mail the corresponding author} ; Antti V. Vä ; hä ; kangas^a ; ^b ; ^{antti.vahakangas@iki.fi" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35A23 ; 26D15 ; 46E35
• 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：330-364
• 全文大小：609 K

文摘

We establish both sufficient and necessary conditions for the validity of the so-called Hardy–Sobolev inequalities on open sets of the Euclidean space. These inequalities form a natural interpolating scale between the (weighted) Sobolev inequalities and the (weighted) Hardy inequalities. The Assouad dimension of the complement of the open set turns out to play an important role in both sufficient and necessary conditions.