Extension and embedding theorems for Campanato spaces on $C^{0,\gamma }$ domains

We consider Campanato spaces with exponents $\lambda ,p$ on domains of class $C^{0,\gamma }$ in the N-dimensional Euclidean space endowed with a natural anisotropic metric depending on $\gamma$. We discuss several results including the appropriate Campanato’s embedding theorem and we prove that functions of those spaces can be extended to the whole of the Euclidean space without deterioration of the exponents $\lambda ,p$.