Geometric Fourier analysis

Cordoba, Antonio. "Geometric Fourier analysis." Annales de l'institut Fourier 32.3 (1982): 215-226. <http://eudml.org/doc/74547>.

@article{Cordoba1982,
abstract = {In this paper we continue the study of the Fourier transform on $\{\bf R\}^n$, $n\ge 2$, 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 $\{\bf R\}^2$. The second is an extension of the Hardy-Littlewood maximal function when one consider cylinders of $\{\bf R\}^n$, $n\ge 2$, of fixed eccentricity and direction on a given curve. We obtain sharp estimates for the $L^2$-norm of such operators.},
author = {Cordoba, Antonio},
journal = {Annales de l'institut Fourier},
keywords = {almost-orthogonality; Fourier transform; Hardy-Littlewood maximal function; sharp estimates for the L2-norm},
language = {eng},
number = {3},
pages = {215-226},
publisher = {Association des Annales de l'Institut Fourier},
title = {Geometric Fourier analysis},
url = {http://eudml.org/doc/74547},
volume = {32},
year = {1982},
}

TY - JOUR
AU - Cordoba, Antonio
TI - Geometric Fourier analysis
JO - Annales de l'institut Fourier
PY - 1982
PB - Association des Annales de l'Institut Fourier
VL - 32
IS - 3
SP - 215
EP - 226
AB - In this paper we continue the study of the Fourier transform on ${\bf R}^n$, $n\ge 2$, 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 ${\bf R}^2$. The second is an extension of the Hardy-Littlewood maximal function when one consider cylinders of ${\bf R}^n$, $n\ge 2$, of fixed eccentricity and direction on a given curve. We obtain sharp estimates for the $L^2$-norm of such operators.
LA - eng
KW - almost-orthogonality; Fourier transform; Hardy-Littlewood maximal function; sharp estimates for the L2-norm
UR - http://eudml.org/doc/74547
ER -