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STRONG VARIATIONAL AND JUMP INEQUALITIES IN HARMONIC ANALYSIS
"... Abstract. We prove variational and jump inequalities for a large class of linear operators arising in harmonic analysis. 1. ..."
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Cited by 24 (1 self)
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Abstract. We prove variational and jump inequalities for a large class of linear operators arising in harmonic analysis. 1.
L p estimates for the biest II. The Fourier case
"... Abstract. We prove L p estimates (Theorem 1.2) for the “biest”, a trilinear multiplier operator with singular symbol. The methods used are based on the treatment of the Walsh analogue of the biest in the prequel [16] of this paper, but with additional technicalities due to the fact that in the Fouri ..."
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Cited by 20 (10 self)
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Abstract. We prove L p estimates (Theorem 1.2) for the “biest”, a trilinear multiplier operator with singular symbol. The methods used are based on the treatment of the Walsh analogue of the biest in the prequel [16] of this paper, but with additional technicalities due to the fact that in the Fourier model one cannot obtain perfect localization in both space and frequency.
Modulation spaces and a class of bounded multilinear pseudodifferential operators
 J. OPERATOR THEORY
, 2003
"... We show that multilinear pseudodifferential operators with symbols in the modulation space M ∞,1 are bounded on products of modulation spaces. In particular, M ∞,1 includes nonsmooth symbols. Several multilinear Calderón– Vaillancourttype theorems are then obtained by using certain embeddings of c ..."
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Cited by 17 (8 self)
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We show that multilinear pseudodifferential operators with symbols in the modulation space M ∞,1 are bounded on products of modulation spaces. In particular, M ∞,1 includes nonsmooth symbols. Several multilinear Calderón– Vaillancourttype theorems are then obtained by using certain embeddings of classical function spaces into modulation spaces.
Use of abstract Hardy spaces, Real interpolation and Applications to bilinear operators.
, 2008
"... This paper can be considered as the sequel of [6], where the authors have proposed an abstract construction of Hardy spaces H 1. They shew an interpolation result for these Hardy spaces with the Lebesgue spaces. Here we describe a more precise result using the real interpolation theory and we clarif ..."
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Cited by 11 (8 self)
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This paper can be considered as the sequel of [6], where the authors have proposed an abstract construction of Hardy spaces H 1. They shew an interpolation result for these Hardy spaces with the Lebesgue spaces. Here we describe a more precise result using the real interpolation theory and we clarify the use of Hardy spaces. Then with the help of the bilinear interpolation theory, we then give applications to study bilinear operators on Lebesgue spaces. These ideas permit us to study singular operators with singularities similar to those of bilinear CalderónZygmund operators in a far more abstract framework as in the euclidean case.
On maximal functions for MikhlinHörmander multipliers
 Adv. Math
"... Abstract. Given MikhlinHörmander multipliers mi, i = 1,..., N, with uniform estimates we prove an optimal p log(N + 1) bound in L p for the maximal function sup i F −1 [mi b f]  and related bounds for maximal functions generated by dilations. These improve results in [7]. Given a symbol m satisfy ..."
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Cited by 9 (3 self)
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Abstract. Given MikhlinHörmander multipliers mi, i = 1,..., N, with uniform estimates we prove an optimal p log(N + 1) bound in L p for the maximal function sup i F −1 [mi b f]  and related bounds for maximal functions generated by dilations. These improve results in [7]. Given a symbol m satisfying 1.
ON THE BOUNDEDNESS OF BILINEAR OPERATORS ON PRODUCTS OF BESOV AND LEBESGUE SPACES
"... Abstract. We prove mapping properties of the form T: B ˙ α1,q1 p1 × L p2 → B ˙ α2,q2 p3 and T: B ˙ α1,q1 p1 × ˙ B α2,q2 p2 → Lp3, for certain related indices p1, p2, p3, q1, q2, α1, α2 ∈ R, where T is a bilinear HörmanderMihlin multiplier or a molecular paraproduct. Applications to bilinear Little ..."
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Cited by 8 (3 self)
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Abstract. We prove mapping properties of the form T: B ˙ α1,q1 p1 × L p2 → B ˙ α2,q2 p3 and T: B ˙ α1,q1 p1 × ˙ B α2,q2 p2 → Lp3, for certain related indices p1, p2, p3, q1, q2, α1, α2 ∈ R, where T is a bilinear HörmanderMihlin multiplier or a molecular paraproduct. Applications to bilinear LittlewoodPaley theory are discussed. 1.
L p estimates for the biest I. The Walsh case
"... Abstract. We prove L p estimates (Theorem 1.8) for the Walsh model of the “biest”, a trilinear multiplier with singular symbol. The corresponding estimates for the Fourier model will be obtained in the sequel [15] of this paper. 1. introduction The bilinear Hilbert transform can be written (modulo m ..."
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Cited by 8 (6 self)
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Abstract. We prove L p estimates (Theorem 1.8) for the Walsh model of the “biest”, a trilinear multiplier with singular symbol. The corresponding estimates for the Fourier model will be obtained in the sequel [15] of this paper. 1. introduction The bilinear Hilbert transform can be written (modulo minor modifications) as
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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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.
TRANSFERENCE OF BILINEAR MULTIPLIER OPERATORS On Lorentz Spaces
, 2007
"... Let m(ξ, η) be a bounded continuous function in IR × IR, 0 < pi, qi < ∞ for i = 1,2 and 0 < p3, q3 ≤ ∞ where 1/p1+1/p2 = 1/p3. It is shown that ..."
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Cited by 7 (1 self)
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Let m(ξ, η) be a bounded continuous function in IR × IR, 0 < pi, qi < ∞ for i = 1,2 and 0 < p3, q3 ≤ ∞ where 1/p1+1/p2 = 1/p3. It is shown that