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

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Abstract

In this article we give necessary and sufficient conditions for the boundedness of the weighted Hardy-Cesà 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-Cesàro operator with symbols in the Lipschitz space on the weighted Morrey-Herz space are also established.

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Authors and Affiliations

  1. Institute of Mathematics, Vietnamese Academy of Science and Technology, Hanoi, Vietnam

    N. M. Chuong

  2. Department of Basic Sciences, Mientrung University of Civil Engineering, 24 Nguyen Du, Tuy Hoa City, Phu Yen, Vietnam

    D. V. Duong

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  1. N. M. Chuong
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  2. D. V. Duong
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Correspondence to N. M. Chuong.

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Chuong, N.M., Duong, D.V. The p-adic weighted Hardy-Cesàro operators on weighted Morrey-Herz space. P-Adic Num Ultrametr Anal Appl 8, 204–216 (2016). https://doi.org/10.1134/S207004661603002X

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