 Morrey–Campanato space

Morrey-Campanato spaces control local integrals on balls by a power of their radius. The Morrey form uses ${\sup }_{x,r}{r}^{-\lambda }{\int }_{B_r(x)}|u{|}^p$; the Campanato space uses $|u-u_{B_r(x)}{|}^p$ instead. Mean subtraction measures oscillation and relates this family to Hölder spaces.

Morrey–Campanato spaces are function spaces that generalize several important concepts in analysis, particularly in the study of differentiability properties of functions and partial differential equations. They are named after the mathematicians Carlo Morrey and Mario Campanato, who contributed to their development.