Refined Sobolev inequalities in Lorentz spaces

Hajer Bahouri (1) , Cohen Albert (2)

1 EDP
2 LJLL - Laboratoire Jacques-Louis Lions

We establish refined Sobolev inequalities between the Lorentz spaces and homogeneous Besov spaces. The sharpness of these inequalities is illustrated on several examples, in particular based on non-uniformly oscillating functions known as chirps. These results are also used to derive refined Hardy inequalities.

Domaines: Equations aux dérivées partielles [math.AP]

Hajer Bahouri, Cohen Albert. Refined Sobolev inequalities in Lorentz spaces. Journal of Fourier Analysis and Applications, 2011, 17 (4), pp.662-673. ⟨hal-00795960⟩