The p-Adic Weighted Hardy-Cesàro Operators on Weighted Morrey-Herz Space

摘要

In this article we give necessary and sufficient conditions for the boundedness of the weighted Hardy-Cesàro operators which is associated to the parameter curve γ(t, x) = γ(t)x defined by U_(ψ,γ)f(x) = ∫_(Z_p~?)f(γ(t)x)ψ(t)dt on the weighted Morrey-Herz space over the p-adic field. Especially, the corresponding operator norms are established in each case. These results actually extend those of K. S. Rim and J. Lee [27] and of the authors [9]. Moreover, the sufficient conditions of boundedness of commutators of p-adic weighted Hardy-Cesàro operator with symbols in the Lipschitz space on the weighted Morrey-Herz space are also established.