The Marcinkiewicz multiplier condition for bilinear operators

Details The Marcinkiewicz multiplier condition for bilinear operators The Marcinkiewicz multiplier condition for bilinear operators

2000-10-08

arxiv.org/abs/math/0010076v1

Mathematics

Functional Analysis

42 pages

Scientific paper

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.

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