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62
Nahmod A., Boundedness of bilinear operators with nonsmooth symbols
, 2000
"... Abstract. We announce the L pboundedness 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 eal ..."
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Cited by 12 (0 self)
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Abstract. We announce the L pboundedness 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 CoifmanMeyer for smooth multipliers and ones, such the Bilinear Hilbert transform of LaceyThiele, where the multiplier is not smooth.
On multilinear oscillatory integrals, nonsingular and singular
 Duke Math. J
"... Abstract. Basic questions concerning nonsingular multilinear operators with oscillatory factors are posed and partially answered. L p norm inequalities are established for multilinear integral operators of CalderónZygmund type which incorporate oscillatory factors e iP, where P is a realvalued pol ..."
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Cited by 10 (5 self)
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Abstract. Basic questions concerning nonsingular multilinear operators with oscillatory factors are posed and partially answered. L p norm inequalities are established for multilinear integral operators of CalderónZygmund type which incorporate oscillatory factors e iP, where P is a realvalued polynomial. Consider multilinear functionals (1.1) Λλ(f1, f2, · · · , fn) =
ON THE HÖRMANDER CLASSES OF BILINEAR PSEUDODIFFERENTIAL OPERATORS
, 2010
"... Bilinear pseudodifferential operators with symbols in the bilinear analog of all the Hörmander classes are considered and the possibility of a symbolic calculus for the transposes of the operators in such classes is investigated. Precise results about which classes are closed under transposition a ..."
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Cited by 10 (4 self)
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Bilinear pseudodifferential operators with symbols in the bilinear analog of all the Hörmander classes are considered and the possibility of a symbolic calculus for the transposes of the operators in such classes is investigated. Precise results about which classes are closed under transposition and can be characterized in terms of asymptotic expansions are presented. This work extends the results for more limited classes studied before in the literature and, hence, allows the use of the symbolic calculus (when it exists) as an alternative way to recover the boundedness on products of Lebesgue spaces for the classes that yield operators with bilinear CalderónZygmund kernels. Some boundedness properties for other classes with estimates in the form of Leibniz’ rule are presented as well.
The Hörmander multiplier theorem for multilinear operators
 J. Reine Angew. Math. (2012
"... Abstract. In this paper, we provide a version of the MihlinHörmander multiplier theorem for multilinear operators in the case where the target space is L p for p ≤ 1. This extends a recent result of Tomita [15] who proved an analogous result for p> 1. 1. ..."
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Abstract. In this paper, we provide a version of the MihlinHörmander multiplier theorem for multilinear operators in the case where the target space is L p for p ≤ 1. This extends a recent result of Tomita [15] who proved an analogous result for p> 1. 1.
Local estimates and global continuities in Lebesgue spaces for bilinear operators
, 2008
"... In this paper, we first prove some local estimates for bilinear operators (closely related to the bilinear Hilbert transform and similar singular operators) with truncated symbol. Such estimates, in accordance with the Heisenberg uncertainty principle correspond to a description of “offdiagonal ” d ..."
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Cited by 9 (4 self)
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In this paper, we first prove some local estimates for bilinear operators (closely related to the bilinear Hilbert transform and similar singular operators) with truncated symbol. Such estimates, in accordance with the Heisenberg uncertainty principle correspond to a description of “offdiagonal ” decay. In addition they allow us to prove global continuities in Lebesgue spaces for bilinear operators with spatial dependent symbol.
BILINEAR MULTIPLIERS AND TRANSFERENCE
, 2005
"... We give de Leeuwtype transference theorems for bilinear multipliers. In particular, it is shown that bilinear multipliers arising from regulated functions m(ξ,η)inR × R can be transferred to bilinear multipliers acting on T × T and Z × Z. The results follow from the description of bilinear multipli ..."
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Cited by 6 (1 self)
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We give de Leeuwtype transference theorems for bilinear multipliers. In particular, it is shown that bilinear multipliers arising from regulated functions m(ξ,η)inR × R can be transferred to bilinear multipliers acting on T × T and Z × Z. The results follow from the description of bilinear multipliers on the discrete real line acting on L pspaces.
Carleson measures, trees, EXTRAPOLATION, AND T(b) THEOREMS
, 2001
"... The theory of Carleson measures, stopping time arguments, and atomic decompositions has been wellestablished in harmonic analysis. More recent is the theory of phase space analysis from the point of view of wave packets on tiles, tree selection algorithms, and tree size estimates. The purpose of th ..."
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Cited by 5 (1 self)
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The theory of Carleson measures, stopping time arguments, and atomic decompositions has been wellestablished in harmonic analysis. More recent is the theory of phase space analysis from the point of view of wave packets on tiles, tree selection algorithms, and tree size estimates. The purpose of this paper is to demonstrate that the two theories are in fact closely related, by taking existing results and reproving them in a unified setting. In particular we give a dyadic version of extrapolation for Carleson measures, as well as a twosided local dyadic T(b) theorem which generalizes earlier T(b)
A bilinear pseudodifferential calculus.
, 2008
"... In this paper, we are interested in the construction of a bilinear pseudodifferential calculus. We define some symbolic classes which contains those of CoifmanMeyer. These new classes allow us to consider operators closely related to the bilinear Hilbert transform. We give a description of the acti ..."
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In this paper, we are interested in the construction of a bilinear pseudodifferential calculus. We define some symbolic classes which contains those of CoifmanMeyer. These new classes allow us to consider operators closely related to the bilinear Hilbert transform. We give a description of the action of our bilinear operators on Sobolev spaces. These classes also have a “nice ” behavior through the transposition and the composition operations that we will present. Key words: multilinear pseudodifferential calculus, timefrequency analysis, asymptotic expansion.