Generalized Campanato space over non‐homogeneous space and its applications

Abstract The authors introduce generalized Campanato space with regularized condition over non‐homogeneous space, and study its basic properties including the John–Nirenberg inequality and equivalent characterizations. As applications, the boundedness of fractional type Marcinkiewicz integral and its commutator on generalized Morrey space over non‐homogeneous space is obtained.