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Boundedness of weighted Hardy operator and its adjoint on Triebel-Lizorkin-type spaces. (English) Zbl 1242.46046
Summary: Let p[1,], q[1,), τ(0,), and α(0,1) such that τ>1/p-1/q and αn(1/p-τ), let U ψ be the weighted Hardy operator and V ψ its adjoint operator with respect to the weight function ψ. In this paper, the authors establish a sufficient and necessary condition on the weight function ψ to ensure the boundedness of U ψ and V ψ on the Triebel-Lizorkin-type spaces F ˙ p,q α,τ ( n ) and their predual spaces, Triebel-Lizorkin-Hausdorff spaces, which unify and generalize the known results on Q-type spaces.
MSC:
46E35Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
47B38Operators on function spaces (general)