Compactness of Hardy–Steklov operator

Pair of weights u, v is characterized so that the Hardy–Steklov operator (Tf )(x) = b(x) a(x) f (t)dt is compact between weighted Lebesgue spaces Lp(u) and Lq (v), where 1 < p,q < ∞, a, b are certain increasing functions and f 0. The compactness of the conjugate operator (T ∗f )(x) = a−1(x) b−1(x) f (t)dt is also studied.  2003 Elsevier Inc. All rights reserved