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Multilinear multipliers associated to simplexes of arbitrary length
, 2007
"... In this article we prove that the n linear operator whose symbol is the characteristic function of the simplex ∆n=ξ1<...<ξn is bounded from L 2 ×... × L 2 into L 2/n, generalizing in this way our previous work on the “biest ” operator [12], [13] (which corresponds to the case n=3) as well a ..."
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In this article we prove that the n linear operator whose symbol is the characteristic function of the simplex ∆n=ξ1<...<ξn is bounded from L 2 ×... × L 2 into L 2/n, generalizing in this way our previous work on the “biest ” operator [12], [13] (which corresponds to the case n=3) as well as the LaceyThiele theorem on the bilinear Hilbert transform [7], [8] (which corresponds to the case n=2).
GENERALIZATIONS OF THE CARLESONHUNT THEOREM I. THE CLASSICAL SINGULARITY CASE
, 2005
"... Abstract. In this article, we prove L p estimates for a general maximal operator, which extend both the classical CoifmanMeyer [2] and CarlesonHunt [1], [7] theorems in harmonic analysis. 1. ..."
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Abstract. In this article, we prove L p estimates for a general maximal operator, which extend both the classical CoifmanMeyer [2] and CarlesonHunt [1], [7] theorems in harmonic analysis. 1.
PARAPRODUCTS WITH FLAG SINGULARITIES I. A CASE STUDY
, 2006
"... In this paper we prove L p estimates for a trilinear operator, whose symbol is given by the product of two standard symbols, satisfying the well known MarcinkiewiczHÃ¶rmanderMihlin condition. Our main result contains in particular the classical CoifmanMeyer theorem. This trilinear operator is ..."
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In this paper we prove L p estimates for a trilinear operator, whose symbol is given by the product of two standard symbols, satisfying the well known MarcinkiewiczHÃ¶rmanderMihlin condition. Our main result contains in particular the classical CoifmanMeyer theorem. This trilinear operator is the simplest example of a large class of multilinear operators, which we called paraproducts with flag singularities.
MAXIMAL BILINEAR SINGULAR INTEGRAL OPERATORS ASSOCIATED WITH DILATIONS OF PLANAR SETS
"... Abstract. We obtain square function estimates and bounds for maximal singular integral operators associated with bilinear multipliers given by characteristic functions of dyadic dilations of certain planar sets. As as consequence, we deduce pointwise almost everywhere convergence for lacunary partia ..."
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Abstract. We obtain square function estimates and bounds for maximal singular integral operators associated with bilinear multipliers given by characteristic functions of dyadic dilations of certain planar sets. As as consequence, we deduce pointwise almost everywhere convergence for lacunary partial sums of bilinear Fourier series with respect to methods of summation determined by the corresponding planar sets. 1.