ON WEIGHTED NORM INTEGRAL INEQUALITY OF G.H. HARDY'S TYPE

In this paper, we give a necessary and sufficient condition on Hardy's integral inequality: integral(X) [T f](p) wd mu <= C integral(X) f(p) upsilon d mu for all f >= 0 (1) where w, upsilon are non-negative measurable functions on X, a non-negative function f defined on (0, infinity), K(x, y) is a non-negative and measurable on X x X , (T f) (x) = integral(infinity)(0) K(x, y) f(y)dy and C is a constant depending on K, p but independent of f. This work is a continuation of our recent result in [9].