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Bilinear square spectral multipliers on stratified groups

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Abstract

In this paper, on stratified groups, we give a reasonable definition of bilinear square spectral multiplier and its commutator. Then we study their boundedness on weighted Lebesgue spaces under the assumption of its weak boundedness and a sum-type Hörmander condition. Besides, we show that, in Euclidean spaces, the smoothness conditions applied to ensure the boundedness of bilinear square Fourier multiplier can be replaced by the sum-type Hörmander condition.

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Acknowledgements

The authors would like to express sincere thanks to the referees for the valuable comments and helpful suggestions.

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Correspondence to Jiman Zhao.

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J. Zhao: The corresponding author, supported by National Natural Science Foundation of China (Grant Nos. 11471040 and 11761131002).

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Fang, J., Zhao, J. Bilinear square spectral multipliers on stratified groups. J. Pseudo-Differ. Oper. Appl. 11, 267–288 (2020). https://doi.org/10.1007/s11868-019-00295-1

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Keywords

  • Bilinear square spectral multiplier
  • Commutator
  • Stratified groups

Mathematics Subject Classification

  • 42B25
  • 43A80
  • 47B40