A multiplier theorem for Fourier series in several variables

Nakhle Asmar¹ ; Florence Newberger² ; Saleem Watson²

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.

Résumé

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.

Détail

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