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This paper is devoted to the characterization of the lack of compactness of the Sobolev embedding of H N (R 2N ) into the Orlicz space using Fourier analysis. The approach adopted in this paper is strikingly different from the one used in 2D in [4, 6, 7] , which consists in tracking the large values of the sequences considered. The analysis we employ in this work is inspired by the strategy of P. Gérard in  and is based on the notion introduced in  of being log-oscillating with respect to a scale.doi:10.4310/mrl.2014.v21.n1.a3 fatcat:vkpdeqktrvbxbcehwp7pszwj2a