The p-adic weighted Hardy-Cesàro operators on weighted Morrey-Herz space

Abstract

In this article we give necessary and sufficient conditions for the boundedness of the weighted Hardy-Cesa ro operators which is associated to the parameter curve γ(t, x) = γ(t)x defined by \({U_{\psi ,\gamma }}f\left( x \right) = \int {\left( {\gamma \left( t \right)x} \right)} \psi \left( t \right)dt\) 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-Cesaro operator with symbols in the Lipschitz space on the weighted Morrey-Herz space are also established.