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We prove interpolation estimates between Morrey-Campanato spaces and Sobolevspaces. These estimates give in particular concentration-compactnessinequalities in the translation-invariant and in the translation- anddilation-invariant case. They also give in particular interpolation estimatesbetween Sobolev spaces and functions of bounded mean oscillation. The proofsrely on Sobolev integral representation formulae and maximal function theory.Fractional Sobolev spaces are also covered.

portugaliae mathematica

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