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Mat. Zametki, 2019, Volume 106, Issue 1, paper published in the English version journal (Mi mz12154)  

Papers published in the English version of the journal

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

N. M. Chuonga, D. V. Duongb, K. H. Dungc

a 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.

Funding Agency Grant Number
National Foundation for Science and Technology Development Vietnam 101.02-2014.51
This research is funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant 101.02-2014.51.

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

Bibliographic databases:

Received: 16.08.2018
Revised: 20.12.2018
Language:

Citation: N. M. Chuong, D. V. Duong, K. H. Dung, “Two-Weighted Inequalities for Hausdorff Operators in Herz-Type Hardy Spaces”, Math. Notes, 106:1 (2019), 20–37

Citation in format AMSBIB
\Bibitem{NguDuoDun19}
\by N.~M.~Chuong, D.~V.~Duong, K.~H.~Dung
\paper Two-Weighted Inequalities for Hausdorff Operators in Herz-Type Hardy Spaces
\jour Math. Notes
\yr 2019
\vol 106
\issue 1
\pages 20--37
\mathnet{http://mi.mathnet.ru/mz12154}
\crossref{https://doi.org/10.1134/S0001434619070034}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000483778800003}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85071637529}


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