This article is concerned with the question of whether Marcinkiewicz multipliers on give rise to bilinear multipliers on ℝⁿ × ℝⁿ. 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm146-2-2,
author = {Loukas Grafakos and Nigel J. Kalton},
title = {The Marcinkiewicz multiplier condition for bilinear operators},
journal = {Studia Mathematica},
volume = {147},
year = {2001},
pages = {115-156},
zbl = {0981.42008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm146-2-2}
}
Loukas Grafakos; Nigel J. Kalton. The Marcinkiewicz multiplier condition for bilinear operators. Studia Mathematica, Tome 147 (2001) pp. 115-156. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm146-2-2/