In between the inequalities of Sobolev and Hardy
Lehrbäck, J., & Vähäkangas, A. (2016). In between the inequalities of Sobolev and Hardy. Journal of Functional Analysis, 271(2), 330-364. https://doi.org/10.1016/j.jfa.2016.04.028
Published inJournal of Functional Analysis
© 2016 Elsevier Inc.
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.
PublisherAcademic Press Inc.
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