Weighted Triebel-Lizorkin and Herz Spaces Estimates for p-Adic Hausdorff Type Operator and its Applications

The aim of this paper is to establish the boundedness of the Hausdorff operator in the Triebel-Lizorkin spaces and Herz spaces with absolutely homogeneous weights and the Muckenhoupt weights on p-adic field. Moreover, the corresponding operator norms are estimated. Some applications to the Hardy, Hilbert and weighted Hardy-Cesàro operators on p-adic field are also shown.