Results 1  10
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20
On the two dimensional Bilinear Hilbert Transform
, 2008
"... We investigate the Bilinear Hilbert Transform in the plane and the pointwise convergence of bilinear averages in Ergodic theory, arising from Z 2 actions. Our techniques combine novel one and a halfdimensional phasespace analysis with more standard onedimensional theory. ..."
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Cited by 18 (4 self)
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We investigate the Bilinear Hilbert Transform in the plane and the pointwise convergence of bilinear averages in Ergodic theory, arising from Z 2 actions. Our techniques combine novel one and a halfdimensional phasespace analysis with more standard onedimensional theory.
The disc as a bilinear multiplier
 Amer. J. Math
"... Abstract. A classical theorem of C. Fefferman [3] says that the characteristic function of the unit disc is not a Fourier multiplier on L p (R 2) unless p = 2. In this article we obtain a result that brings a contrast with the previous theorem. We show that the characteristic function of the unit di ..."
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Cited by 16 (10 self)
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Abstract. A classical theorem of C. Fefferman [3] says that the characteristic function of the unit disc is not a Fourier multiplier on L p (R 2) unless p = 2. In this article we obtain a result that brings a contrast with the previous theorem. We show that the characteristic function of the unit disc in R 2 is the Fourier multiplier of a bounded bilinear operator from L p1 p2 p p1p2 (R) × L (R) intoL(R), when 2 ≤ p1,p2 < ∞ and 1 <p = ≤ 2. The proof p1+p2 of this result is based on a new decomposition of the unit disc and delicate orthogonality and combinatorial arguments. This result implies norm convergence of bilinear Fourier series and strengthens the uniform boundedness of the bilinear Hilbert transforms, as it yields uniform vectorvalued bounds for families of bilinear Hilbert transforms. 1.
NEW UNIFORM BOUNDS FOR A WALSH MODEL OF THE BILINEAR HILBERT TRANSFORM
"... The notion of bilinear Hilbert transform usually refers to a member of a family of bilinear operators parameterized by a unit vector β perpendicular to (1, 1, 1). We will write the bilinear operators in this family more symmetrically as dual trilinear forms Λβ, acting on three ..."
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Cited by 11 (3 self)
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The notion of bilinear Hilbert transform usually refers to a member of a family of bilinear operators parameterized by a unit vector β perpendicular to (1, 1, 1). We will write the bilinear operators in this family more symmetrically as dual trilinear forms Λβ, acting on three
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.
Uniform estimates on paraproducts
 Journal d’Analyse de Jerusalem 87 (2002) 369–384. MR1945289 (2004a:42023), Zbl 1043.42012
"... Dedicated to our late friend and admired mathematician Tom Wolff Abstract. We prove uniform L p estimates (Theorem 1.1) for a family of paraproducts and corresponding maximal operators. 1. ..."
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Cited by 7 (0 self)
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Dedicated to our late friend and admired mathematician Tom Wolff Abstract. We prove uniform L p estimates (Theorem 1.1) for a family of paraproducts and corresponding maximal operators. 1.
Modulation invariant bilinear T(1) theorem
 J. Anal. Math
"... Abstract. We prove a T(1) theorem for bilinear singular integral operators (trilinear forms) with a onedimensional modulation symmetry. 1. ..."
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Cited by 5 (3 self)
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Abstract. We prove a T(1) theorem for bilinear singular integral operators (trilinear forms) with a onedimensional modulation symmetry. 1.
BILINEAR MULTIPLIERS ON LORENTZ SPACES
, 710
"... Abstract. We give one sufficient and two necessary conditions for boundedness between Lebesgue or Lorentz spaces of several classes of bilinear multiplier operators closely connected with the bilinear Hilbert transform. 1. Introduction. The bilinear Hilbert transform with parameter α ∈ R is the oper ..."
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Cited by 5 (3 self)
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Abstract. We give one sufficient and two necessary conditions for boundedness between Lebesgue or Lorentz spaces of several classes of bilinear multiplier operators closely connected with the bilinear Hilbert transform. 1. Introduction. The bilinear Hilbert transform with parameter α ∈ R is the operator given by Hα(f, g)(x) = 1
Uniform estimates for the bilinear Hilbert transform
 II, Revista Mat. Iberoamericana
, 2006
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IMPROVED RANGE IN THE RETURN TIMES THEOREM
, 2009
"... We prove that the Return Times Theorem holds true for pairs of L p − L q functions, whenever 1/p + 1/q < 3/2. ..."
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Cited by 3 (0 self)
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We prove that the Return Times Theorem holds true for pairs of L p − L q functions, whenever 1/p + 1/q < 3/2.