Boundedness of weighted Hardy operator and its adjoint on Triebel-Lizorkin-type spaces. (English) Zbl 1242.46046
Summary: Let , , , and such that and , let be the weighted Hardy operator and its adjoint operator with respect to the weight function . In this paper, the authors establish a sufficient and necessary condition on the weight function to ensure the boundedness of and on the Triebel-Lizorkin-type spaces and their predual spaces, Triebel-Lizorkin-Hausdorff spaces, which unify and generalize the known results on -type spaces.
|46E35||Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems|
|47B38||Operators on function spaces (general)|