A counterexample for Improved Sobolev Inequalities over the 2-adic group

On the framework of the 2-adic group Z_2, we study a Sobolev-like inequality where we estimate the L^2 norm by a geometric mean of the BV norm and the Besov space B(-1,\infty,\infty) norm. We first show, using the special topological properties of the p-adic groups, that the set of functions of bounded variations BV can be identified to the Besov space B(1,\infty,1). This identification lead us to the construction of a counterexample to the improved Sobolev inequality.Comment: 10

A remark on Besov spaces interpolation over the 2-adic group

Motivated by a recent result which identifies in the special setting of the 2-adic group the Besov space $\dot{B}^{1,\infty}_{1}(\mathbb{Z}_2)$ with $BV(\mathbb{Z}_2)$, the space of function of bounded variation, we study in this article some functional relationships between Besov spaces.Comment: 6 page

A molecular method applied to a non-local PDE in stratified Lie groups

In this article we study a transport-diffusion equation in the framework of the stratified Lie groups. For this equation we will study the existence of the solutions, a maximum principle, a positivity principle and H\"older regularity.Comment: 26 pages. arXiv admin note: substantial text overlap with arXiv:1205.2834, arXiv:1007.391

Non-local diffusion equations with L\'evy-type operators and divergence free drift

We are interested in some properties related to the solutions of non-local diffusion equations with divergence free drift. Existence, maximum principle and a positivity principle are proved. In order to study Holder regularity, we apply a method that relies in the Holder-Hardy spaces duality and in the molecular characterisation of local Hardy spaces. In these equations, the diffusion is given by L\'evy-type operators with an associated L\'evy measure satisfying some upper and lower bounds.Comment: arXiv admin note: substantial text overlap with arXiv:1007.391

Improved Sobolev Inequalities and Muckenhoupt weights on stratified Lie groups

We study in this article the Improved Sobolev inequalities with Muckenhoupt weights within the framework of stratified Lie groups. This family of inequalities estimate the Lq norm of a function by the geometric mean of two norms corresponding to Sobolev spaces W(s;p) and Besov spaces B(-b, infty, infty). When the value p which characterizes Sobolev space is strictly larger than 1, the required result is well known in R^n and is classically obtained by a Littlewood-Paley dyadic blocks manipulation. For these inequalities we will develop here another totally different technique. When p = 1, these two techniques are not available anymore and following M. Ledoux in R^n, we will treat here the critical case p = 1 for general stratified Lie groups in a weighted functional space setting. Finally, we will go a step further with a new generalization of Improved Sobolev inequalities using weak-type Sobolev spaces.Comment: 17 page

A complementary view to the bonding pattern in the N5 +cation an electron localization function and local temperature analysis

Indexación: ScieloThe electron localization function (ELF), a local measure of the Pauli repulsion effect, and the local Kohn-Sham temperature analysis, which is defined within the framework of a local thermodynamics description of density functional theory, have been used to explore the bonding characteristics in the open chain N5+ cation. It is found that both the ELF and local temperature maps depict uniquely the regions of pair localizations, yielding a description of bonding which agrees and complements previous techniques of analysis. Particularly, the three-center four-electron interaction in the NNN terminal atoms of N5+ and the contribution of terminal triple bonds to the bonding nature of the cation have been characterized in detail from the electron fluctuation among ELF basins populations. The features of bonding in terms of the local kinetic energy analysis have been visualized directly from the analysis of local temperature map.http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0717-97072003000400010&lang=p

Gap solitons and symmetry breaking in parity-time symmetric microring CROWs

The propagation properties of optical fields in linear and nonlinear parity-time symmetric microring coupled resonator optical waveguides are studied. The effects described include the existence of symmetry breaking thresholds, the propagation of gap solitons in nonlinear transmission lines and the existence of quasi stable propagation regimes outside the broken symmetry regions.Comment: Final Versio