A multiplier theorem for Fourier series in several variables

Nakhle Asmar, Florence Newberger, and Saleem Watson. "A multiplier theorem for Fourier series in several variables." Colloquium Mathematicae 106.2 (2006): 221-230. <http://eudml.org/doc/283457>.

@article{NakhleAsmar2006,
abstract = {We define a new type of multiplier operators on $L^\{p\}(^N)$, where $^N$ is the N-dimensional torus, and use tangent sequences from probability theory to prove that the operator norms of these multipliers are independent of the dimension N. Our construction is motivated by the conjugate function operator on $L^\{p\}(^N)$, to which the theorem applies as a particular example.},
author = {Nakhle Asmar, Florence Newberger, Saleem Watson},
journal = {Colloquium Mathematicae},
keywords = {Fourier multiplier operator; martingale difference decomposition; conjugate function; tangent sequence},
language = {eng},
number = {2},
pages = {221-230},
title = {A multiplier theorem for Fourier series in several variables},
url = {http://eudml.org/doc/283457},
volume = {106},
year = {2006},
}

TY - JOUR
AU - Nakhle Asmar
AU - Florence Newberger
AU - Saleem Watson
TI - A multiplier theorem for Fourier series in several variables
JO - Colloquium Mathematicae
PY - 2006
VL - 106
IS - 2
SP - 221
EP - 230
AB - We define a new type of multiplier operators on $L^{p}(^N)$, where $^N$ is the N-dimensional torus, and use tangent sequences from probability theory to prove that the operator norms of these multipliers are independent of the dimension N. Our construction is motivated by the conjugate function operator on $L^{p}(^N)$, to which the theorem applies as a particular example.
LA - eng
KW - Fourier multiplier operator; martingale difference decomposition; conjugate function; tangent sequence
UR - http://eudml.org/doc/283457
ER -