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arXiv · 1011.0970

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

Diego Chamorro
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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.

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Diego Chamorro. 2010-11-03. A counterexample for Improved Sobolev Inequalities over the 2-adic group. https://arxiv.org/abs/1011.0970

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