Improved Sobolev inequalities: the case p = 1 and generalizations to classical Lorentz spaces - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2015

Improved Sobolev inequalities: the case p = 1 and generalizations to classical Lorentz spaces

Résumé

We give a general treatment of refined Sobolev inequalities in the case p = 1 and when p > 1 we study these inequalities using as base space classical Lorentz spaces associated to a weight from the Ariño-Muckenhoupt class Bp. The arguments used for the case p = 1 rely essentially on spectral theory while the ideas behind the case p > 1 are based on pointwise estimates and on the boundedness of Hardy-Littlewood maximal function. As a by-product we will also consider Morrey-Sobolev inequalities. This 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. Improved Sobolev inequalities: the case p = 1 and generalizations to classical Lorentz spaces. 2015. ⟨hal-01148723v1⟩
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