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http://dx.doi.org/10.4134/CKMS.2013.28.2.231

A COUNTEREXAMPLE FOR IMPROVED SOBOLEV INEQUALITIES OVER THE 2-ADIC GROUP  

Chamorro, Diego (Laboratoire d'Analyse et de Probabilites Universite d'Evry Val d'Essonne)
Publication Information
Communications of the Korean Mathematical Society / v.28, no.2, 2013 , pp. 231-241 More about this Journal
Abstract
On the framework of the 2-adic group $\mathcal{Z}_2$, we study a Sobolev-like inequality where we estimate the $L^2$ norm by a geometric mean of the BV norm and the $\dot{B}_{\infty}^{-1,{\infty}}$ 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 ˙$\dot{B}_1^{1,{\infty}}$. This identification lead us to the construction of a counterexample to the improved Sobolev inequality.
Keywords
Sobolev inequalities; p-adic groups;
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