A Fourier approach to the profile decomposition in Orlicz spaces

Hajer Bahouri, Galina Perelman
2014 Mathematical Research Letters  
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 [13] and is based on the notion introduced in [8] of being log-oscillating with respect to a scale.
doi:10.4310/mrl.2014.v21.n1.a3 fatcat:vkpdeqktrvbxbcehwp7pszwj2a