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Maximal operators and singular integrals on the weighted Lorentz and Morrey spaces

  • Nguyen Minh ChuongEmail author
  • Dao Van Duong
  • Kieu Huu Dung
Article
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Abstract

In this paper, we first give some new characterizations of Muckenhoupt type weights through establishing the boundedness of maximal operators on the weighted Lorentz and Morrey spaces. Secondly, we establish the boundedness of sublinear operators including many interesting in harmonic analysis and its commutators on the weighted Morrey spaces. Finally, as an application, the boundedness of strongly singular integral operators and commutators with symbols in BMO space are also given.

Keywords

Maximal function Sublinear operator Strongly singular integral Commutator \(A_p\) weight \(A(p{, } 1)\) weight \(A_p(\varphi )\) weight BMO space Lorentz spaces Morrey spaces 

Mathematics Subject Classification

42B20 42B25 42B99 

Notes

Acknowledgements

The authors are grateful to the anonymous referee for the valuable suggestions and comments which lead to the improvement of the paper. The authors are supported by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No 101.02-2014.51.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of Mathematics, Vietnamese Academy of Science and TechnologyHanoiVietnam
  2. 2.School of Mathematics, Mientrung University of Civil EngineeringPhu YenVietnam
  3. 3.School of Mathematics, University of Transport and CommunicationsHanoiVietnam

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