A counterexample for Improved Sobolev Inequalities over the 2-adic group
Analysis of PDEs
2010-11-04 v1 Functional Analysis
Abstract
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.
Cite
@article{arxiv.1011.0970,
title = {A counterexample for Improved Sobolev Inequalities over the 2-adic group},
author = {Diego Chamorro},
journal= {arXiv preprint arXiv:1011.0970},
year = {2010}
}
Comments
10 p