Functional Inequalities in Stratified Lie groups with Sobolev, Besov, Lorentz and Morrey spaces

2015/05/22 by Chamorro, Diego, Marcoci, Anca-Nicoleta, Marcoci, Liviu-Gabriel
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1505.05986

Abstract

The study of Sobolev inequalities can be divided in two cases: p = 1 and 1 < p < +∞. In the case p = 1 we study here a relaxed version of refined Sobolev inequalities. When p > 1, using as base space classical Lorentz spaces associated to a weight from the Arino-Muckenhoupt class Bp, we will study Gagliardo-Nirenberg inequalities. As a by-product we will also consider Morrey-Sobolev inequalities. These arguments can be generalized to many different frameworks, in particular the proofs are given in the setting of stratified Lie groups.

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