A multiplier theorem for Fourier series in several variables

Volume 106 / 2006

Nakhle Asmar, Florence Newberger, Saleem Watson Colloquium Mathematicum 106 (2006), 221-230 MSC: Primary 42B15; Secondary 60G42. DOI: 10.4064/cm106-2-4

Abstract

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.

Authors

  • Nakhle AsmarMathematics Department
    University of Missouri
    Columbia, MO 65211, U.S.A.
    e-mail
  • Florence NewbergerDepartment of Mathematics and Statistics
    California State University
    Long Beach, CA 90840, U.S.A.
    e-mail
  • Saleem WatsonDepartment of Mathematics and Statistics
    California State University
    Long Beach, CA 90840, U.S.A.
    e-mail

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