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BILINEAR OPERATORS ON HOMOGENEOUS GROUPS
"... Let H p denote the Lebesgue space L p for p>1 and the Hardy space H p for p ≤ 1. For 0 <p,q,r<∞, we study H p × H q → H r mapping properties of bilinear operators given by finite sums of products of Calderón–Zygmund operators on stratified homogeneous Lie groups. When r ≤ 1, we show that su ..."
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Let H p denote the Lebesgue space L p for p>1 and the Hardy space H p for p ≤ 1. For 0 <p,q,r<∞, we study H p × H q → H r mapping properties of bilinear operators given by finite sums of products of Calderón–Zygmund operators on stratified homogeneous Lie groups. When r ≤ 1, we show
Bilinear operators with nonsmooth symbol
 I, J. Fourier Anal. Appl
"... � � � This paper proves the L pboundedness of general bilinear operators associated to a symbol or multiplier which need not be smooth. The Main Theorem establishes a general result for multipliers that are allowed to have singularities along the edges of a cone as well as possibly at its vertex. ..."
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Cited by 29 (3 self)
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� � � This paper proves the L pboundedness of general bilinear operators associated to a symbol or multiplier which need not be smooth. The Main Theorem establishes a general result for multipliers that are allowed to have singularities along the edges of a cone as well as possibly at its vertex
REPRESENTATION AND EXTENSION OF ORTHOREGULAR BILINEAR OPERATORS
, 2007
"... In this paper we study some important structural properties of orthosymmetric bilinear operators using the concept of the square of an Archimedean vector lattice. Some new results on extension and analytical representation of such operators are presented. ..."
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Cited by 7 (6 self)
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In this paper we study some important structural properties of orthosymmetric bilinear operators using the concept of the square of an Archimedean vector lattice. Some new results on extension and analytical representation of such operators are presented.
COMPACT BILINEAR OPERATORS AND COMMUTATORS
, 2013
"... Abstract. A notion of compactness in the bilinear setting is explored. Moreover, commutators of bilinear CalderónZygmund operators and multiplication by functions in a certain subspace of the space of functions of bounded mean oscillations are shown to be compact. 1. ..."
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Abstract. A notion of compactness in the bilinear setting is explored. Moreover, commutators of bilinear CalderónZygmund operators and multiplication by functions in a certain subspace of the space of functions of bounded mean oscillations are shown to be compact. 1.
ON SOME PROPERTIES OF ORTHOSYMMETRIC BILINEAR OPERATORS
, 2008
"... This note contains some properties of positive orthosymmetric bilinear operators on vector lattices which are well known for almost falgebra multiplication but despite of their simplicity does not seem appeared in the literature. ..."
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This note contains some properties of positive orthosymmetric bilinear operators on vector lattices which are well known for almost falgebra multiplication but despite of their simplicity does not seem appeared in the literature.
The Marcinkiewicz multiplier condition for bilinear operators
 Studia Math. 146 (2001), 115–156. LOUKAS GRAFAKOS
"... Abstract. This article is concerned with the question of whether Marcinkiewicz multipliers on R2n give rise to bilinear multipliers on Rn × Rn.We show that this is not always the case. Moreover we find necessary and sufficient conditions for such bilinear multipliers to be bounded. These conditions ..."
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Cited by 28 (8 self)
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in particular imply that a slight logarithmic modification of the Marcinkiewicz condition gives multipliers for which the corresponding bilinear operators are bounded on products of Lebesgue and Hardy spaces. 1.
Discretization versus transference for bilinear operators
 CONTEMPORARY MATHEMATICS
, 2006
"... A very general transference method for bilinear operators is presented and used to show that discretization techniques can also be obtained from transference methods. It is applied to show the boundedness of the discrete version of the bilinear fractional operator and the bisublinear HardyLittlewo ..."
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Cited by 3 (3 self)
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A very general transference method for bilinear operators is presented and used to show that discretization techniques can also be obtained from transference methods. It is applied to show the boundedness of the discrete version of the bilinear fractional operator and the bisublinear Hardy
Bilinear operators and the power series for the Weierstrass sigma function.
 J. Phys. A: Math. Gen
, 2000
"... We use the bilinear operator formalism to derive a new representation of the power series for the Weierstrass # function. ..."
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Cited by 14 (6 self)
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We use the bilinear operator formalism to derive a new representation of the power series for the Weierstrass # function.
HÖLDER TYPE INEQUALITIES FOR Orthosymmetric Bilinear Operators
, 2007
"... An interplay between squares of vector lattice and homogeneous functional calculus is considered and Hölder type inequalities for orthosymmetric bilinear operators are obtained. ..."
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An interplay between squares of vector lattice and homogeneous functional calculus is considered and Hölder type inequalities for orthosymmetric bilinear operators are obtained.
Results 1  10
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821