A multiplier theorem for Fourier series
in several variables
Colloquium Mathematicum, Tome 106 (2006) no. 2, pp. 221-230
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We define a new type of multiplier
operators on $L^p(\mathbb T^N)$, where $\mathbb T^N$ 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 $L^p(\mathbb T^N)$, to which the theorem applies as a particular
example.
Keywords:
define type multiplier operators mathbb where mathbb n dimensional torus tangent sequences probability theory prove operator norms these multipliers independent dimension construction motivated conjugate function operator mathbb which theorem applies particular example
Affiliations des auteurs :
Nakhle Asmar 1 ; Florence Newberger 2 ; Saleem Watson 2
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author = {Nakhle Asmar and Florence Newberger and Saleem Watson},
title = {A multiplier theorem for {Fourier} series
in several variables},
journal = {Colloquium Mathematicum},
pages = {221--230},
publisher = {mathdoc},
volume = {106},
number = {2},
year = {2006},
doi = {10.4064/cm106-2-4},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm106-2-4/}
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%0 Journal Article %A Nakhle Asmar %A Florence Newberger %A Saleem Watson %T A multiplier theorem for Fourier series in several variables %J Colloquium Mathematicum %D 2006 %P 221-230 %V 106 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/cm106-2-4/ %R 10.4064/cm106-2-4 %G en %F 10_4064_cm106_2_4
Nakhle Asmar; Florence Newberger; Saleem Watson. A multiplier theorem for Fourier series in several variables. Colloquium Mathematicum, Tome 106 (2006) no. 2, pp. 221-230. doi: 10.4064/cm106-2-4
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