Radial Fourier multipliers in high dimensions

Yaryong Heo Department of Mathematics, University of Wisconsin, Madison Fëdor Nazarov Department of Mathematics, University of Wisconsin, Madison Andreas Seeger Department of Mathematics, University of Wisconsin, Madison

Functional Analysis mathscidoc:1701.12001

Acta Mathematica, 206, (1), 55-92, 2009.2
Given a fixed$p$≠2, we prove a simple and effective characterization of all radial multipliers of $ \mathcal{F}{L^p}\left( {{\mathbb{R}^d}} \right) $ , provided that the dimension$d$is sufficiently large. The method also yields new$L$^{$q$}space-time regularity results for solutions of the wave equation in high dimensions.
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@inproceedings{yaryong2009radial,
  title={Radial Fourier multipliers in high dimensions},
  author={Yaryong Heo, Fëdor Nazarov, and Andreas Seeger},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203356060409735},
  booktitle={Acta Mathematica},
  volume={206},
  number={1},
  pages={55-92},
  year={2009},
}
Yaryong Heo, Fëdor Nazarov, and Andreas Seeger. Radial Fourier multipliers in high dimensions. 2009. Vol. 206. In Acta Mathematica. pp.55-92. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203356060409735.
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