Hardy-Steklov Operators and the Duality Principle in Weighted First-Order Sobolev Spaces on the Real Axis

摘要

Estimates of the norms of spaces associated to weighted first-order Sobolev spaces with various weight functions and summation parameters are established. As the main technical tool, boundedness criteria for the Hardy-Steklov integral operator with variable limits of integration in Lebesgue spaces on the real axis are used.