ABSTRACT
This chapter investigates the bounded mean oscillation (BMO) space since it is a fundamental function space. It handles operators made up of BMO functions and defines Morrey–Campanato spaces. It includes an auxiliary observation to Morrey–Campanato spaces, shows that Morrey–Campanato spaces are isomorphic to known function spaces. Commutators will play a key role when elliptic differential equations are considered. Especially, commutators generated by BMO and singular integral operators will arise as the solution operators of the elliptic differential equations. The chapter considers commutators generated by BMO and singular integral operators and commutators generated by BMO and fractional integral operators, respectively. In 1938, C. Morrey investigated the elliptic differential operators. His technique became the theory of normed spaces. However, around the 1960’s, S. Campanato proposed a different approach.
