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A multiplier theorem for Fourier series in several variables

Nakhle Asmar; Florence Newberger; Saleem Watson — 2006

Colloquium Mathematicae

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.

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