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

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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.

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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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Correspondence to Nguyen Minh Chuong.

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Minh Chuong, N., Van Duong, D. & Huu Dung, K. Maximal operators and singular integrals on the weighted Lorentz and Morrey spaces. J. Pseudo-Differ. Oper. Appl. 11, 201–228 (2020). https://doi.org/10.1007/s11868-019-00277-3

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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