Decomposition theorems and conjugate pair in D K spaces

Let K be a right-continuous and nondecreasing function. A function f analytic in the unit disk D belongs to the space D k if .D|f.(z)|2K(1.|z|2)dA(z)<.. Decomposition theorems for D k spaces are established in this paper. As an application, we obtain a characterization of interpolation by functions in D k spaces. Furthermore, we characterize functions in D k spaces by conjugate pairs.