EMBEDDINGS BETWEEN WEIGHTED COPSON AND CESARO FUNCTION SPACES

In this paper, characterizations of the embeddings between weighted Copson function spaces Cop(p1,q1)(u(1),v(1)) and weighted Cesaro function spaces Ces(p2,q2) (u(2) , v(2)) are given. In particular, two-sided estimates of the optimal constant c in the inequality (integral(infinity)(0) (integral(t)(0) f(tau)(p2)v2(tau)d tau)(q2/p2) u2(t)dt)(1/q2)& para;& para;<= c(integral(infinity)(0) (integral(t)infinity f(tau)(p1)v1(tau)d tau)(q1/p1) u1(t)dt)(1/q1), where p(1), p(2), q(1), q(2) is an element of (0,infinity), p(2) <= q(2) and u(1), u(2), v(1), v(2) are weights on (0,infinity) are obtained. The most innovative part consists of the fact that possibly different parameters p1 and p2 and possibly different inner weights v(1) and v(2) are allowed. The proof is based on the combination of duality techniques with estimates of optimal constants of the embeddings between weighted Cesaro and Copson spaces and weighted Lebesgue spaces, which reduce the problem to the solutions of iterated Hardy-type inequalities.