Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2010.11.08
  • Published : 2013.04.30
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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.

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References

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