Sobolev embeddings into spaces of Campanato, Morrey, and Hölder type (Q1399380)

The authors consider necessary and sufficient conditions on a rearrangement-invariant Banach function space on a cube \(Q\) in \(\mathbb{R}^n\), \(n\geq 2\) for the corresponding Sobolev space \(W^1X(Q)\) to be continuously embedded into (generalized) Campanato, Morrey, or Hölder spaces. The optimal such r.i. spaces \(X(Q)\) are found. As a by-product, sharp inclusion relations are proved among Campanato, Morrey and Hölder type spaces.