Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4589667 | Journal of Functional Analysis | 2016 | 35 Pages |
Abstract
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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Juha Lehrbäck, Antti V. Vähäkangas,