Bahouri, Hajer; Perelman, Galina A Fourier approach to the profile decomposition in Orlicz spaces. (English) Zbl 1311.46030 Math. Res. Lett. 21, No. 1, 33-54 (2014). Summary: This paper is devoted to the characterization of the lack of compactness of the Sobolev embedding of \(H^N(\mathbb R^{2N})\) into the Orlicz space using Fourier analysis. The approach adopted in this paper is strikingly different from the one used in 2D, 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 [ESAIM, Control Optim. Calc. Var. 3, 213–233 (1998; Zbl 0907.46027)] and is based on the notion introduced in [H. Bahouri, Trends in Mathematics, 1–15 (2013; Zbl 1291.46030)] of being log-oscillating with respect to a scale. Cited in 10 Documents MSC: 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) Keywords:Orlicz space; lack of compactness; profile decomposition; Sobolev embedding Citations:Zbl 0907.46027; Zbl 1291.46030 PDFBibTeX XMLCite \textit{H. Bahouri} and \textit{G. Perelman}, Math. Res. Lett. 21, No. 1, 33--54 (2014; Zbl 1311.46030) Full Text: DOI arXiv