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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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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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 55, 189–209 (2021). https://doi.org/10.1007/s11118-020-09853-5
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DOI: https://doi.org/10.1007/s11118-020-09853-5