The Marcinkiewicz multiplier condition for bilinear operators

Volume 146 / 2001

Loukas Grafakos, Nigel J. Kalton Studia Mathematica 146 (2001), 115-156 MSC: Primary 42B15, 42B20, 42B30; Secondary 46B70, 47G30. DOI: 10.4064/sm146-2-2

Abstract

This article is concerned with the question of whether Marcinkiewicz multipliers on ${\mathbb R}^{2n}$ give rise to bilinear multipliers on ${\mathbb R}^n\times {\mathbb R}^n$. We show that this is not always the case. Moreover, we find necessary and sufficient conditions for such bilinear multipliers to be bounded. These conditions in particular imply that a slight logarithmic modification of the Marcinkiewicz condition gives multipliers for which the corresponding bilinear operators are bounded on products of Lebesgue and Hardy spaces.

Authors

  • Loukas GrafakosDepartment of Mathematics
    University of Missouri-Columbia
    Columbia, MO 65211, U.S.A.
    e-mail
  • Nigel J. KaltonDepartment of Mathematics
    University of Missouri-Columbia
    Columbia, MO 65211, U.S.A.
    e-mail

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