Leibniz-Type Rules for Bilinear and Biparameter Fourier Multiplier Operators with Applications

Abstract

We establish Leibniz-type rules for bilinear and biparameter Fourier multiplier operators with limited Sobolev regularity. Applications of our result are given including the biparameter Leibniz rules, smoothing properties of bilinear-biparameter fractional integrals, and mapping properties of scattering operators for a system of PDEs.

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Acknowledgements

The authors would like to thank the anonymous referee for his/her careful reading the manuscript and providing invaluable corrections and suggestions, which improve their original manuscript.

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Correspondence to Jiexing Yang.

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This research is supported by the National Natural Science Foundation of China (Grant No. 11671397).

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Yang, J., Liu, Z. & Wu, X. Leibniz-Type Rules for Bilinear and Biparameter Fourier Multiplier Operators with Applications. Potential Anal (2020). https://doi.org/10.1007/s11118-020-09853-5

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Keywords

  • Bilinear and biparameter Fourier multiplier
  • Smoothing properties
  • Leibniz-type rules

Mathematics Subject Classification (2010)

  • Primary 42B20
  • Secondary 42B15, 47G99