Morrey-Campanato space

In mathematics, the Morrey–Campanato spaces (named after Charles B. Morrey, Jr. and Sergio Campanato) ${\displaystyle L^{\lambda ,p}(\Omega )}$ are Banach spaces which extend the notion of functions of bounded mean oscillation, describing situations where the oscillation of the function in a ball is proportional to some power of the radius other than the dimension. They are used in the theory of elliptic partial differential equations, since for certain values of ${\displaystyle \lambda }$, elements of the space ${\displaystyle L^{\lambda ,p}(\Omega )}$ are Hölder continuous functions over the domain ${\displaystyle \Omega }$.

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