We define a new type of multiplier operators on , where 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 , to which the theorem applies as a particular example.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm106-2-4,
author = {Nakhle Asmar and Florence Newberger and Saleem Watson},
title = {A multiplier theorem for Fourier series in several variables},
journal = {Colloquium Mathematicae},
volume = {106},
year = {2006},
pages = {221-230},
zbl = {1162.42304},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm106-2-4}
}
Nakhle Asmar; Florence Newberger; Saleem Watson. A multiplier theorem for Fourier series in several variables. Colloquium Mathematicae, Tome 106 (2006) pp. 221-230. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm106-2-4/