Generalized Campanato spaces with variable growth condition (Harmonic Analysis and Nonlinear Partial Differential Equations)

Abstract

This is a survey on generalized Campanato spaces with variable growth condition. We first define generalized Campanato spaces and related function spaces. Then we state the relations among these function spaces and the characterization of pointwise multipliers on generalized Campanato spaces. Next we state the boundedness of singular integral operators and the convolution operator with the heat kernel. We also give an application of generalized Campanato spaces to the Cauchy problem for the Navier‐Stokes equation. Finally, we state the boundedness of the commutators generated by functions in generalized Campanato spaces.