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

2010/11/03 by Diego Chamorro, Chamorro, Diego
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #math.AP #math.FA

paper · pdf · doi:10.48550/arxiv.1011.0970

10 p

arxiv created 2010/11/03 · arxiv updated 2010/11/04

Abstract

On the framework of the 2-adic group Z₂, we study a Sobolev-like inequality where we estimate the L² norm by a geometric mean of the BV norm and the Besov space B(-1,∞,∞) 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,∞,1). This identification lead us to the construction of a counterexample to the improved Sobolev inequality.

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