Hardy type inequalities involving suprema

Subject Integral equations and integral transforms
Title Hardy type inequalities involving suprema
Author(s) A.M. Abylayeva, A.O. Baiarystanov
Keywords Hardy type inequalities, Oinarov condition, integral operators.
Abstract Let I = (a; b), -  a < b  , 1 p; q, w is a nonnegative, continuous function on I, and uq, vp are nonnegative locally integrable functions on I, and the function v–p’ is also locally integrable on I. Let us introduce the operators R_∞^+ f(x)=sup┬(a