Article

Journal of Geometric Analysis

, Volume 21, Issue 1, pp 96-117

On Radial and Conical Fourier Multipliers

  • Yaryong HeoAffiliated withDepartment of Mathematics, University of Wisconsin-Madison
  • , Fëdor NazarovAffiliated withDepartment of Mathematics, University of Wisconsin-Madison
  • , Andreas SeegerAffiliated withDepartment of Mathematics, University of Wisconsin-Madison Email author 

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Abstract

We investigate connections between radial Fourier multipliers on ℝ d and certain conical Fourier multipliers on ℝ d+1. As an application we obtain a new weak type endpoint bound for the Bochner–Riesz multipliers associated with the light cone in ℝ d+1, where d≥4, and results on characterizations of L p L p inequalities for convolutions with radial kernels.

Keywords

Radial Fourier multipliers Cone multiplier Weak type estimates

Mathematics Subject Classification (2000)

42B15