Mathematical Research Letters

Volume 21 (2014)

Number 1

A Fourier approach to the profile decomposition in Orlicz spaces

Pages: 33 – 54

DOI: http://dx.doi.org/10.4310/MRL.2014.v21.n1.a3

Authors

Hajer Bahouri (Laboratoire d’Analyse et de Mathématiques Appliquées, Université Paris-Est, Créteil, France)

Galina Perelman (Laboratoire d’Analyse et de Mathématiques Appliquées, Université Paris-Est, Créteil, France)

Abstract

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 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.

Keywords

Orlicz, lack of compactness, profile decomposition

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