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Functional Inequalities in Stratified Lie Groups with Sobolev, Besov, Lorentz and Morrey Spaces

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Abstract

When \(p>1\), using as base space classical Lorentz spaces associated to a weight from the Ariño–Muckenhoupt class \(B_p\), 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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Notes

  1. The lower bound \(N\ge 4\) corresponds to the homogeneous dimension of the Heisenberg group \(\mathbb {H}^1\), which is the simplest non-trivial stratified Lie group.

  2. Which means that the Lie algebra generated by the family \({\textbf {X}}\) is \(\mathfrak {g}\).

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Acknowledgements

A part of this work was performed while the second and third authors visited the University of Evry Val d’Essonne. We express our gratitude to the Laboratoire de Mathématiques et Modélisation d’Evry (LaMME) of the University of Evry Val d’Essonne for the hospitality and excellent conditions.

Funding

The second named author was partially supported by POSDRU/159/1.5/S/137750.

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Authors and Affiliations

  1. Laboratoire de Mathématiques et Modélisation d’Evry (LaMME) - UMR 8071, Université d’Evry Val d’Essonne, 23 Boulevard de France, 91037, Evry Cedex, France

    Diego Chamorro

  2. Department of Mathematics and Computer Science, Technical University of Civil Engineering, Bld. Lacul Tei, No. 124, Sector 2., Bucharest, Romania

    Anca-Nicoleta Marcoci & Liviu-Gabriel Marcoci

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  1. Diego Chamorro
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  2. Anca-Nicoleta Marcoci
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  3. Liviu-Gabriel Marcoci
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Correspondence to Liviu-Gabriel Marcoci.

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Chamorro, D., Marcoci, AN. & Marcoci, LG. Functional Inequalities in Stratified Lie Groups with Sobolev, Besov, Lorentz and Morrey Spaces. Results Math 78, 219 (2023). https://doi.org/10.1007/s00025-023-01991-7

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