Hankel forms and sums of random variables

Volume 176 / 2006

Henry Helson Studia Mathematica 176 (2006), 85-92 MSC: 43A15, 30B50, 15A63. DOI: 10.4064/sm176-1-6

Abstract

A well known theorem of Nehari asserts on the circle group that bilinear forms in $H^2$ can be lifted to linear functionals on $H^1$. We show that this result can be extended to Hankel forms in infinitely many variables of a certain type. As a corollary we find a new proof that all the $L^p$ norms on the class of Steinhaus series are equivalent.

Authors

  • Henry HelsonMathematics Department
    University of California
    Berkeley, CA 94720-3840, U.S.A.
    e-mail

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