The Marcinkiewicz multiplier condition for bilinear operators
Volume 146 / 2001
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.
