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

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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https://hal.archives-ouvertes.fr/hal-01148723
Contributor : Diego Chamorro <>
Submitted on : Saturday, December 15, 2018 - 10:46:48 AM
Last modification on : Thursday, December 20, 2018 - 1:18:26 AM
Long-term archiving on : Saturday, March 16, 2019 - 1:11:09 PM

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  • HAL Id : hal-01148723, version 3
  • ARXIV : 1505.05986

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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. 2018. ⟨hal-01148723v3⟩

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