Limiting Sobolev and Hardy inequalities on stratified homogeneous groups

Abstract

We give a sufficient condition for limiting Sobolev and Hardy inequalities to hold on stratified homogeneous groups. In the Euclidean case, this condition reduces to the known cancelling necessary and sufficient condition. We obtain in particular endpoint Korn--Sobolev and Korn--Hardy inequalities on stratified homogeneous groups.

To appear in Ann. Fenn. Math

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