ABSTRACT
This chapter discusses how to replace the condition for a derivative belonging to M1p(Rn). It investigates the bounded mean oscillation (BMO) space since it is a fundamental function space. The chapter 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 we consider elliptic differential equations. Especially, commutators generated by BMO and singular integral operators will arise as the solution operators of the elliptic differential equations. In 1938, C. Morrey investigated the elliptic differential operators. His technique became the theory of normed spaces. Quite often, the Morrey norm has an equivalent expression to this Campanato technique. The chapter establishes that Morrey spaces and Campanato spaces are equivalent.
