## On radial Fourier multipliers |

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### Contents

Chapter I Section 1 | 4 |

Chapter I Section 2 | 8 |

Chapter II Section 1 | 16 |

2 other sections not shown

### Common terms and phrases

A.W. Khapp asymptotic estimate Bessel functions Bochner-Riesz means bounded by C2k bounded function break the region C(RQ Chapter characteristic function Charles Fefferman completes the proof concerns the boundedness continuous derivatives convolution counterexample decrease at infinity defined denotes developed by Hirschman E.M. Stein exists a constant extends the range faster than cosine Fefferman and Stein following lemma Fourier transform functions f g(R+e Hilbert transform lim sup Lp classes Lp(tRn mean value theorem measurable function multiplier of Lp operators of IRn oscillates no faster Peter Anthony Tomas problems prove the estimate prove the following q conjugate R+e)k radial Fourier multipliers radial function radial multiplier radial Schwartz function rectangle region of integration restriction theorem Section 2 Let semisimple Lie group show that T+ smooth function suffices to prove suffices to show supremum techniques developed thesis triangle inequality unbounded uniformly bounded multipliers unit disc weakly against Schwartz