This article is cited in 14 papers

Papers published in the English version of the journal

Two-Weighted Inequalities for Hausdorff Operators in Herz-Type Hardy Spaces

N. M. Chuong^a, D. V. Duong^b, K. H. Dung<sup>c

a</sup> Institute of Mathematics, Vietnamese Academy of Science and Technology, Hanoi, 100000 Vietnam
^b School of Mathematics, Mientrung University of Civil Engineering, Phu Yen, 620000 Vietnam
^c School of Mathematics, University of Transport and Communications, Hanoi, 100000 Vietnam

Abstract: In this paper, we prove the boundedness of matrix Hausdorff operators and rough Hausdorff operators in the two weighted Herz-type Hardy spaces associated with both power weights and Muckenhoupt weights. By applying the fact that the standard infinite atomic decomposition norm on two weighted Herz-type Hardy spaces is equivalent to the finite atomic norm on some dense subspaces of them, we generalize some previous known results due to Chen et al. [7] and Ruan, Fan [31].

Keywords: Hausdorff operator, Herz space, Herz-type Hardy space, $A_p$ weight, atom.

Received: 16.08.2018
Revised: 20.12.2018

Language: English

 English version: Mathematical Notes, 2019, 106:1, 20–37

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