Boundedness of Weighted Hardy Operator and Its Adjoint on Triebel-Lizorkin-Type Spaces

摘要

Letp∈[1,∞],q∈[1,∞),τ∈(0,∞), andα∈(0,1)such thatτ>1/p-1/qandα≤n(1/p-τ), letUψbe the weighted Hardy operator andVψits adjoint operator with respect to the weight functionψ. In this paper, the authors establish a sufficient and necessary condition on weight functionψto ensure the boundedness ofUψandVψon the Triebel-Lizorkin-type spacesḞp,qα,τ(ℝn)and their predual spaces, Triebel-Lizorkin-Hausdorff spaces, which unify and generalize the known results onQ-type spaces.