The Marcinkiewicz multiplier condition for bilinear operators

Loukas Grafakos, Nigel J. Kalton
2001 Studia Mathematica  
This article is concerned with the question of whether Marcinkiewicz multipliers on R 2n give rise to bilinear multipliers on R n ×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
more » ... esgue and Hardy spaces. 2000 Mathematics Subject Classification: Primary 42B15, 42B20, 42B30; Secondary 46B70, 47G30.
doi:10.4064/sm146-2-2 fatcat:jdgt4bi3sbd6jgg2rrdlpcuwly