## Lectures on Fourier series of several variables |

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### Contents

2 RiemannLebesgue Theorem | 3 |

3 Localization theorem | 4 |

DiniLipschitz test | 11 |

28 other sections not shown

### Common terms and phrases

2Trm Abel mean Applying assume Banach Banach space bounded function C(Tn characteristic function continuous function continuously embedded converges uniformly defined denote domain doubly invariant everywhere exists a constant exists a function f e H formula Fourier coefficients Fourier series Fourier transform function f Hardy-Littlewood harmonic functions holomorphic im«x inequality integrable function interpolation theorem invariant subspace kernel Lebesgue Lemma Let f e linear localization property log w dx log+ LP(Rn LP(Tn measurable function n-harmonic non-negative non-tangential limit non-tangentially bounded norm normalized conjugate one-dimensional open set Poisson kernel polydisk positive measure Proof of Theorem prove restrictedly non-tangentially Riesz-Bochner right hand side satisfies sequence simply invariant sphere spherical means square partial sums strong type summability Suppose Theorem 18 Theorem 29 trigonometric polynomial weak type zero