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2 RiemannLebesgue Theorem
3 Localization theorem
28 other sections not shown
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