A counterexample for improved Sobolev inequalities over the 2-adic group
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On the framework of the 2-adic group Z2, we study a Sobolevlikeinequality where we estimate the L2 norm by a geometric mean of theBV norm and the ˙B−1,∞∞ norm. We first show, using the special topologicalproperties of the p-adic groups, that the set of functions of boundedvariations BV can be identified to the Besov space ˙B1,∞1 . This identificationlead us to the construction of a counterexample to the improvedSobolev inequality.
Abstract
On the framework of the 2-adic group Z2, we study a Sobolevlikeinequality where we estimate the L2 norm by a geometric mean of theBV norm and the ˙B−1,∞∞ norm. We first show, using the special topologicalproperties of the p-adic groups, that the set of functions of boundedvariations BV can be identified to the Besov space ˙B1,∞1 . This identificationlead us to the construction of a counterexample to the improvedSobolev inequality.
참고문헌 (14)
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