Compactness of Hardy-Steklov operator

[摘要] Pair of weights u, v is characterized so that the Hardy-Steklov operator (Tf)(x) = integral(a(x))(b(x)) is compact between weighted Lebesgue spaces L-p (u) and L-q (V), where 1 < p, q < infinity, a, b are certain increasing functions and f greater than or equal to 0. The compactness of the conjugate operator (T*f)(x) integral(b-1(x))(a-1(x)) f(t) dt is also studied.

[发布日期] 2003-12-15

[关键词] Hardy operator;Hardy-Steklov operator;Hardy inequality compactness;boundedness