Mathematical Research Letters

Volume 7 (2000)

Number 6

Boundedness of Bilinear Operators with nonsmooth symbols

Pages: 767 – 778

DOI: http://dx.doi.org/10.4310/MRL.2000.v7.n6.a9

Authors

John E. Gilbert (The University of Texas at Austin)

Andrea R. Nahmod (University of Massachusetts)

Abstract

We announce the $L^p$-boundedness of general bilinear operators associated to a symbol or multiplier which need not be smooth. We establish a general result for multipliers that are allowed to have singularities along the edges of a cone as well as possibly at its vertex. It thus unifies ealier results of Coifman-Meyer for smooth multipliers and ones, such the Bilinear Hilbert transform of Lacey-Thiele, where the multiplier is not smooth.

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