Sobolev norm estimates for a class of bilinear multipliers

@article{Bernicot2013SobolevNE,
  title={Sobolev norm estimates for a class of bilinear multipliers},
  author={Fr{\'e}d{\'e}ric Bernicot and Vjekoslav Kovavc},
  journal={arXiv: Classical Analysis and ODEs},
  year={2013}
}
We consider bilinear multipliers that appeared as a distinguished particular case in the classification of two-dimensional bilinear Hilbert transforms by Demeter and Thiele [9]. In this note we investigate their boundedness on Sobolev spaces. Furthermore, we study structurally similar operators with symbols that also depend on the spatial variables. The new results build on the existing L^p estimates for a paraproduct-like operator previously studied by the authors in [5] and [10]. Our primary… 

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