The Marcinkiewicz multiplier condition for bilinear operators

Loukas Grafakos¹ ; Nigel J. Kalton¹

¹Department of Mathematics University of Missouri-Columbia Columbia, MO 65211, U.S.A.

Studia Mathematica, Tome 146 (2001) no. 2, pp. 115-156

Résumé

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.

Détail

DOI : 10.4064/sm146-2-2

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