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Transference on certain multilinear multiplier operators

Part of: Harmonic analysis in several variables

Published online by Cambridge University Press:  09 April 2009

Dashan Fan  and
Shuichi Sato
Dashan Fan
Affiliation:
Department of Mathematics Huazhong University of Science and Technology and Department of Mathematics University of Wisconsin-MilwaukeeMilwaukee, WI 53201USA e-mail: fan@csd.uwm.edu
Shuichi Sato
Affiliation:
Department of Mathematics Kanazawa UniversityKanazawa 920-11Japan e-mail: shuichi@kenroku.kanazawa-u.ac.jp
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Abstract

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We study DeLeeuw type theorems for certain multilinear operators on the Lebesgue spaces and on the Hardy spaces. As applications, on the torus we obtain an analog of Lacey—Thiele's theorem on the bilinear Hilbert transform, as well as analogies of some recent theorems on multilinear singular integrals by Kenig—Stein and by Grafakos—Torres.

MSC classification

Secondary: 42B15: Multipliers 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B25: Maximal functions, Littlewood-Paley theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 70 , Issue 1 , February 2001 , pp. 37 - 55
Copyright
Copyright © Australian Mathematical Society 2001

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