Zeitschrift für Analysis und ihre Anwendungen


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Volume 35, Issue 4, 2016, pp. 489–504
DOI: 10.4171/ZAA/1575

Published online: 2016-10-05

Bounds for the Weighted Hardy-Cesàro Operator and its Commutator on Morrey-Herz Type Spaces

Nguyen Minh Chuong[1], Dao Van Duong[2] and Ha Duy Hung[3]

(1) Vietnam Academy of Science and Technology, Hanoi, Vietnam
(2) Central University of Construction, Phu Yen, Vietnam
(3) Ton Duc Thang University, Ho Chi Minh City, Vietnam

In this paper we will prove the boundedness of weighted Hardy-Cesàro operator on Herz and Morrey-Herz spaces with absolutely homogeneous weights. The corresponding operator norms are obtained. We also prove the boundedness of the commutators of Hardy-Cesàro operator on weighted spaces of Morrey-Herz type, with their symbols belong to Lipschitz space. By these we extend and strengthen previous results due to Kuang [15], Fu et al. [9] and Tang et al. [20].

Keywords: Hardy-Cesàro operator, Hardy-Littlewood average operator, Morrey-Herz spaces

Chuong Nguyen Minh, Duong Dao Van, Hung Ha Duy: Bounds for the Weighted Hardy-Cesàro Operator and its Commutator on Morrey-Herz Type Spaces. Z. Anal. Anwend. 35 (2016), 489-504. doi: 10.4171/ZAA/1575