Differences weighted composition operators acting between kind of weighted Bergman-type spaces and the Bers-type space -I

Let O(D) denote the class of all analytic or holomorphic functions on the open unit disk D of C. Let phi and psi are an analytic self-maps of D and u, v is an element of O(D). The difference of two weighted composition operators is defined by ( ) T phi,psi f(z) :=W phi, uf - W psi, vf(z) = u(z)(f degrees phi)(z) - v(z)(f degrees psi)(z), f is an element of O(D) and z is an element of D. The boundedness and compactness of the differences of two weighted composition operators from H alpha infinity(D) spaces into NK(D) spaces ( resp. from NK(D) into H alpha infinity(D)) are investigate in this paper.