## Littlewood-Paley and multiplier theory |

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### Contents

Prologue | 1 |

Convolution Operators ScalarValued Case | 30 |

Convolution Operators VectorValued Case | 50 |

Copyright | |

10 other sections not shown

### Common terms and phrases

Borel bounded function Chapter compact open subgroups completes the proof constant continuous convergence theorem Corollary cosets countable covering family deduce defined definition denote disconnected groups dual group dyadic decomposition element establish every/in f\dm finite measure finite subsets follows Fourier series Fourier transform Fubini-Tonelli theorem Fubini's theorem functions g Haar measure Hadamard decomposition Hence Hilbert transform Holder's inequality implies integrable function L2 n LP LCA group Lemma linear Littlewood-Paley theorem LP and WM LP property Lp(G majorised mapping Marcinkiewicz interpolation theorem Marcinkiewicz theorem martingale measurable functions multiplier operator multiplier theorem norm number Cp pairwise disjoint Parseval formula partial sum positive integer positive number proof of Theorem Rademacher functions Riesz theorem Sj)JeZ Steckin suffices to prove suitable family Suppose theory tion trigonometric polynomial type A(p weak type