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

被引：14

作者：

Chuong N.M. ^{[1
]}

Duong D.V. ^{[2
]}

机构：

[1] Institute of Mathematics, Vietnamese Academy of Science and Technology, Hanoi

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

来源：

P-Adic Numbers, Ultrametric Analysis, and Applications | 2016年 / 8卷 / 3期

关键词：

commutator; p-adic analysis; Weighted Hardy-Cesàro operator; weighted Morrey-Herz space;

D O I：

10.1134/S207004661603002X

中图分类号：

学科分类号：

摘要：

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 Uψ, ᵞ f(x) = ʃʃ*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. © 2016, Pleiades Publishing, Ltd.

引用

页码：204 / 216

页数：12

共 36 条

[1]

Albeverio S., Karwowski W., A randomwalk on p-adics: the generator and its spectrum, Stoch. Process. Appl., 53, pp. 1-22, (1994)

[2]

Albeverio S., Khrennikov A.Y., Shelkovich V.M., Harmonic analysis in the p-adic Lizorkin spaces: fractional operators, pseudo-differential equations, p-wavelets, Tauberian theorems, J. Fourier Anal. Appl., 12, 4, pp. 393-425, (2006)

[3]

Avetisov A.V., Bikulov A.H., Kozyrev S.V., Osipov V.A., p-Adic models of ultrametric diffusion constrained by hierarchical energy landscapes, J. Phys. A:Math. Gen., 35, pp. 177-189, (2002)

[4]

Avetisov A.V., Bikulov A.H., Osipov V.A., p-Adic description of characteristic relaxation in complex systems, J. Phys. A:Math. Gen., 36, pp. 4239-4246, (2003)

[5]

Andersen K.F., Muckenhoupt B., Weighted weak type Hardy inequalities with applications to Hilbert transforms and maximal functions, Studia Math., 72, 1, pp. 9-26, (1982)

[6]

Carton-Lebrun C., Fosset M., Moyennes et quotients de Taylor dans BMO, Bull. Soc. Roy. Sci. Lié ge, 53, 2, pp. 85-87, (1994)

[7]

Coifman R.R., Rochberg R., Weiss G., Factorization theorems for Hardy spaces in several variables, Ann.Math., 103, pp. 611-635, (1976)

[8]

Chuong N.M., Egorov Y.V., Khrennikov A.Y., Meyer Y., Mumford D., Harmonic, Wavelet and p-Adic Analysis, (2007)

[9]

Chuong N.M., Duong D.V., Weighted Hardy-Littlewood operators and commutators on p-adic functional spaces, p-Adic Numbers Ultrametric Anal. Appl., 5, 1, pp. 65-82, (2013)

[10]

Chuong N.M., Duong D.V., Wavelet bases in the Lebesgue spaces on the field of p-adic numbers, p-Adic Numbers Ultrametric Anal. Appl., 5, 2, pp. 106-121, (2013)

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