Geodesic
A multiplier theorem for Fourier series in several variables
Nakhle Asmar 1   ; Florence Newberger 2   ; Saleem Watson 2
1 Mathematics Department University of Missouri Columbia, MO 65211, U.S.A.
2 Department of Mathematics and Statistics California State University Long Beach, CA 90840, U.S.A.
Colloquium Mathematicum, Tome 106 (2006) no. 2, pp. 221-230 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm106-2-4
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

Nakhle Asmar  1   ; Florence Newberger  2   ; Saleem Watson  2

1 Mathematics Department University of Missouri Columbia, MO 65211, U.S.A.
2 Department of Mathematics and Statistics California State University Long Beach, CA 90840, U.S.A. 
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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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