Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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CONTINUITY OF THE MAXIMAL COMMUTATORS IN SOBOLEV SPACES

  • Xixi Jiang (College of Mathematics and Systems Science Shandong University of Science and Technology) ;
  • Feng Liu (College of Mathematics and Systems Science Shandong University of Science and Technology)
  • Received : 2023.06.12
  • Accepted : 2023.11.14
  • Published : 2024.05.01
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Abstract

We prove the Sobolev continuity of maximal commutator and its fractional variant with Lipschitz symbols, both in the global and local cases. The main result in global case answers a question originally posed by Liu and Wang in [29].

Keywords

Acknowledgement

The second author was supported partly by the Natural Science Foundation of Shandong Province (Grant no. ZR2023MA022) and the National Natural Science Foundation of China (Grant no. 12326371).

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