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Article Dans Une Revue Results in mathematics = Resultate der Mathematik Année : 2023

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

Résumé

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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Dates et versions

hal-01148723 , version 1 (05-05-2015)
hal-01148723 , version 2 (16-03-2018)
hal-01148723 , version 3 (15-12-2018)

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Diego Chamorro, Anca-Nicoleta Marcoci, Liviu-Gabriel Marcoci. Functional Inequalities in Stratified Lie groups with Sobolev, Besov, Lorentz and Morrey spaces. Results in mathematics = Resultate der Mathematik, 2023, 78 (219). ⟨hal-01148723v3⟩
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