Smoothing estimates for non-dispersive equations

@article{Ruzhansky2015SmoothingEF,
  title={Smoothing estimates for non-dispersive equations},
  author={Michael Ruzhansky and Mitsuru Sugimoto},
  journal={Mathematische Annalen},
  year={2015},
  volume={365},
  pages={241-269}
}
This paper describes an approach to global smoothing problems for non-dispersive equations based on ideas of comparison principle and canonical transformation established in authors’ previous paper (Ruzhansky and Sugimoto, Proc Lond Math Soc, 105:393–423, 2012), where dispersive equations were treated. For operators $$a(D_x)$$a(Dx) of order m satisfying the dispersiveness condition $$\nabla a(\xi )\ne 0$$∇a(ξ)≠0 for $$\xi \not =0$$ξ≠0, the global smoothing estimate $$\begin{aligned} {\left… 

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