Interpolation inequalities between Sobolev and Morrey–Campanato spaces: A common gateway to concentration-compactness and Gagliardo–Nirenberg interpolation inequalities

  • Jean Van Schaftingen

    Université Catholique de Louvain, Belgium

Abstract

We prove interpolation estimates between Morrey–Campanato spaces and Sobolev spaces. These estimates give in particular concentration-compactness inequalities in the translation-invariant and in the translation- and dilation-invariant case. They also give in particular interpolation estimates between Sobolev spaces and functions of bounded mean oscillation. The proofs rely on Sobolev integral representation formulae and maximal function theory. Fractional Sobolev spaces are also covered.

Cite this article

Jean Van Schaftingen, Interpolation inequalities between Sobolev and Morrey–Campanato spaces: A common gateway to concentration-compactness and Gagliardo–Nirenberg interpolation inequalities. Port. Math. 71 (2014), no. 3/4, pp. 159–175

DOI 10.4171/PM/1947