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2,458
Inversion Theorem for Bilinear Hilbert Transform
, 2007
"... An approximation result for the bilinear Hilbert transform is proved and used for the inversion of the bilinear Hilbert transform. Also, pLebesgue points (p ≥ 1) are analyzed. ..."
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An approximation result for the bilinear Hilbert transform is proved and used for the inversion of the bilinear Hilbert transform. Also, pLebesgue points (p ≥ 1) are analyzed.
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.
Distributional Estimates for the Bilinear Hilbert Transform
"... ABSTRACT. We obtain size estimates for the distribution function of the bilinear Hilbert transform acting on a pair of characteristic functions of sets of finite measure, that yield exponential decay at infinity and blowup near zero to the power −2/3 (modulo some logarithmic factors). These results ..."
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Cited by 5 (2 self)
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ABSTRACT. We obtain size estimates for the distribution function of the bilinear Hilbert transform acting on a pair of characteristic functions of sets of finite measure, that yield exponential decay at infinity and blowup near zero to the power −2/3 (modulo some logarithmic factors). These results
Uniform bounds for the bilinear Hilbert transforms
 889–993. MR2113017 (2006e:42011), Zbl 1071.44004. Xiaochun Li
, 2004
"... Abstract. We continue the investigation initiated in [8] of uniform Lp bounds � for the family of bilinear Hilbert transforms Hα,β(f, g)(x) = p.v. f(x − αt)g(x − βt) R dt t. In this work we show that Hα,β map Lp1 (R) × Lp2 (R) into Lp (R) uniformly in the real parameters α, β satisfying  α β − 1  ..."
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Cited by 36 (15 self)
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Abstract. We continue the investigation initiated in [8] of uniform Lp bounds � for the family of bilinear Hilbert transforms Hα,β(f, g)(x) = p.v. f(x − αt)g(x − βt) R dt t. In this work we show that Hα,β map Lp1 (R) × Lp2 (R) into Lp (R) uniformly in the real parameters α, β satisfying  α β − 1
Bilinear Hilbert transform on measure spaces.
"... In this paper we obtain the boundedness of the periodic, discrete and Ergodic bilinear Hilbert transform, from Lp1×Lp2 into Lp3, where 1/p1 + 1/p2 = 1/p3 and pi ≥ 1. The main techniques are a bilinear version of the transference method of Coifman and Weiss and certain discretization of bilinear oper ..."
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Cited by 6 (4 self)
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In this paper we obtain the boundedness of the periodic, discrete and Ergodic bilinear Hilbert transform, from Lp1×Lp2 into Lp3, where 1/p1 + 1/p2 = 1/p3 and pi ≥ 1. The main techniques are a bilinear version of the transference method of Coifman and Weiss and certain discretization of bilinear
Uniform estimates for the bilinear Hilbert transform
 II, Revista Mat. Iberoamericana
, 2006
"... ar ..."
Triangularization of Hankel operators and the bilinear Hilbert transform
 Contemp. Math
, 1999
"... Abstract. A relation between the Bilinear Hilbert transform and triangular truncations of Hankel and Toeplitz operators is established. Boundedness of triangular truncations of Hankel operators then follows from deep, known properties for the Bilinear Hilbert transform, con rming a conjecture attrib ..."
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Cited by 2 (0 self)
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Abstract. A relation between the Bilinear Hilbert transform and triangular truncations of Hankel and Toeplitz operators is established. Boundedness of triangular truncations of Hankel operators then follows from deep, known properties for the Bilinear Hilbert transform, con rming a conjecture
L p estimates for the bilinear Hilbert transform
, 1996
"... For the bilinear Hilbert transform given by H fg(x) = p. v. Z f(x \Gamma y)g(x + y) dy y we announce the inequality kH fgk p3 K p1 ;p 2 kfk p1 kgk p2 , provided 2 ! p 1 ; p 2 ! 1, 1=p 3 = 1=p 1 + 1=p 2 and 1 ! p 3 ! 2. We announce a partial resolution to long standing conjectures concerning th ..."
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Cited by 62 (16 self)
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For the bilinear Hilbert transform given by H fg(x) = p. v. Z f(x \Gamma y)g(x + y) dy y we announce the inequality kH fgk p3 K p1 ;p 2 kfk p1 kgk p2 , provided 2 ! p 1 ; p 2 ! 1, 1=p 3 = 1=p 1 + 1=p 2 and 1 ! p 3 ! 2. We announce a partial resolution to long standing conjectures concerning
MULTILINEAR EXTRAPOLATION AND APPLICATIONS TO THE BILINEAR HILBERT TRANSFORM
"... Abstract. We present two extrapolation methods for multisublinear operators that allow us to derive estimates for general functions from the corresponding estimates on characteristic functions. Of these methods, the first is applicable to general multisublinear operators while the second requires ..."
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Cited by 3 (0 self)
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working with the socalled (ε, δ)atomic operators. Among the applications, we discuss some new endpoint estimates for the bilinear Hilbert transform. 1.
Results 1  10
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2,458