The Marcinkiewicz multiplier condition for bilinear operators

Loukas Grafakos, and Nigel J. Kalton. "The Marcinkiewicz multiplier condition for bilinear operators." Studia Mathematica 146.2 (2001): 115-156. <http://eudml.org/doc/284820>.

@article{LoukasGrafakos2001,
abstract = {This article is concerned with the question of whether Marcinkiewicz multipliers on $ℝ^\{2n\}$ 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.},
author = {Loukas Grafakos, Nigel J. Kalton},
journal = {Studia Mathematica},
keywords = {Marcinkiewicz condition; bilinear multipliers; paraproducts; Littlewood-Paley projection},
language = {eng},
number = {2},
pages = {115-156},
title = {The Marcinkiewicz multiplier condition for bilinear operators},
url = {http://eudml.org/doc/284820},
volume = {146},
year = {2001},
}

TY - JOUR
AU - Loukas Grafakos
AU - Nigel J. Kalton
TI - The Marcinkiewicz multiplier condition for bilinear operators
JO - Studia Mathematica
PY - 2001
VL - 146
IS - 2
SP - 115
EP - 156
AB - This article is concerned with the question of whether Marcinkiewicz multipliers on $ℝ^{2n}$ 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.
LA - eng
KW - Marcinkiewicz condition; bilinear multipliers; paraproducts; Littlewood-Paley projection
UR - http://eudml.org/doc/284820
ER -