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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...

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