Morrey–Campanato space

Summary

Morrey spaces and Campanato spaces measure the size of a function on small balls, uniformly over all centres. A Morrey space asks that the $L^p$ mass of $f$ on a ball of radius $r$ is at most a constant times $r^\lambda$. A Campanato space asks the same of the oscillation of $f$ around its mean on the ball. Special cases are Lebesgue spaces, bounded mean oscillation and Hölder continuous functions. They are a basic tool for the regularity of solutions of elliptic equations.