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

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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 [35].

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Acknowledgments

The authors are grateful to the anonymous referees for their valuable suggestions and comments, which led to the improvement of the paper.

Funding

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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Authors and Affiliations

  1. Institute of Mathematics, Vietnamese Academy of Science and Technology, Hanoi, 100000, Vietnam

    N. M. Chuong

  2. School of Mathematics, Mientrung University of Civil Engineering, Phu Yen, Tuy Hòa, 620000, Vietnam

    D. V. Duong

  3. School of Mathematics, University of Transport and Communications, Hanoi, 100000, Vietnam

    K. H. Dung

Authors
  1. N. M. Chuong
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  2. D. V. Duong
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  3. K. H. Dung
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Correspondence to D. V. Duong.

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Chuong, N.M., Duong, D.V. & Dung, K.H. Two-Weighted Inequalities for Hausdorff Operators in Herz-Type Hardy Spaces. Math Notes 106, 20–37 (2019). https://doi.org/10.1134/S0001434619070034

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  • DOI: https://doi.org/10.1134/S0001434619070034

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