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Geometric Fourier analysis

Antonio Cordoba (1982)

Annales de l'institut Fourier

In this paper we continue the study of the Fourier transform on R n , n 2 , analyzing the “almost-orthogonality” of the different directions of the space with respect to the Fourier transform. We prove two theorems: the first is related to an angular Littlewood-Paley square function, and we obtain estimates in terms of powers of log ( N ) , where N is the number of equal angles considered in R 2 . The second is an extension of the Hardy-Littlewood maximal function when one consider cylinders of R n , n 2 , of fixed eccentricity...

Global orthogonality implies local almost-orthogonality.

J. Michael Wilson (2000)

Revista Matemática Iberoamericana

We introduce a new stopping-time argument, adapted to handle linear sums of noncompactly-supported functions that satisfy fairly weak decay, smoothness, and cancellation conditions. We use the argument to obtain a new Littlewood-Paley-type result for such sums.

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