The Marcinkiewicz multiplier condition for bilinear operators

• Autorzy: Loukas Grafakos , Nigel J. Kalton
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 42B15: Multipliers
• 47G30: Pseudodifferential operators
• 46B70: Interpolation between normed linear spaces
• 42B20: Singular and oscillatory integrals (Calder\'on-Zygmund, etc.)
• 42B30: H p -spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2001
• Tom: 146
• Numer: 2
• Strony: 115-156

Daty

wydano

2001

Twórcy

autor

Loukas Grafakos

• Department of Mathematics, University of Missouri-Columbia, Columbia, MO 65211, U.S.A.

autor

Nigel J. Kalton

• Department of Mathematics, University of Missouri-Columbia, Columbia, MO 65211, U.S.A.

Identyfikatory

DOI

10.4064/sm146-2-2