Juha Lehrbäck, Antti V. Vähäkangas
Published 2015-02-04Version 1
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.
Necessary conditions for the boundedness of fractional operators on variable Lebesgue spaces
Singular Integrals associated with Reflection Groups on Euclidean Space
On volumes determined by subsets of Euclidean space
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