Weighted modular inequalities for Hardy–Steklov operators ✩

We characterize weighted modular inequalities of weak and strong type for the Hardy–Steklov operators T defined by Tf (x) = g(x) h(x) s(x) f (t)dt, where g is a positive function and s, h are increasing and continuous functions such that s(x) h(x) for all x. © 2005 Elsevier Inc. All rights reserved.