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Weighted norm inequalities, offdiagonal estimates and elliptic operators, Part II: Offdiagonal estimates on spaces of homogeneous type
, 2005
"... Abstract. This is the fourth article of our series. Here, we apply the results of [AM1] to study weighted norm inequalities for the Riesz transform of the LaplaceBeltrami operator on Riemannian manifolds and of subelliptic sum of squares on Lie groups, under the doubling volume property and Poincar ..."
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Cited by 27 (10 self)
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Abstract. This is the fourth article of our series. Here, we apply the results of [AM1] to study weighted norm inequalities for the Riesz transform of the LaplaceBeltrami operator on Riemannian manifolds and of subelliptic sum of squares on Lie groups, under the doubling volume property and Poincaré inequalities. 1. Introduction and
Boundedness for multilinear LittlewoodPaley operators on Hardy and HerzHardy spaces
 Extracta Math
"... Let T be a CalderonZygmund operator, a classical result of Coifman, Rochberg and Weiss (see [7]) states that the commutator [b, T] = T (bf)−bTf (where b ∈ BMO(Rn)) is bounded on Lp(Rn) for 1 < p <∞; Chanillo (see [2]) proves a similar result when T is replaced by the fractional integral oper ..."
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Cited by 5 (1 self)
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Let T be a CalderonZygmund operator, a classical result of Coifman, Rochberg and Weiss (see [7]) states that the commutator [b, T] = T (bf)−bTf (where b ∈ BMO(Rn)) is bounded on Lp(Rn) for 1 < p <∞; Chanillo (see [2]) proves a similar result when T is replaced by the fractional integral operator.
WEIGHTED NORM INEQUALITIES FOR FRACTIONAL OPERATORS
, 2007
"... Abstract. We prove weighted norm inequalities for fractional powers of elliptic operators together with their commutators with BMO functions, encompassing what is known for the classical Riesz potentials and elliptic operators with Gaussian domination by the classical heat operator. The method relie ..."
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Cited by 2 (1 self)
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Abstract. We prove weighted norm inequalities for fractional powers of elliptic operators together with their commutators with BMO functions, encompassing what is known for the classical Riesz potentials and elliptic operators with Gaussian domination by the classical heat operator. The method relies upon a goodλ method that does not use any size or smoothness estimates for the kernels. 1.
Weighted boundedness for multilinear singular integral operator with variable CalderónZygmund kernel, African Diaspora
 Authors: Zhiqiang Wang and Lanzhe Liu College of Mathematics Changsha University of Science and Technology Changsha, 410077, P.R.of China Email: lanzheliu@163.com
"... Abstract. In this paper, we prove the boundedness for some multilinear operators generated by singular integral operators and Lipschitz functions on some Hardy and Herz type spaces. ..."
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Cited by 2 (1 self)
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Abstract. In this paper, we prove the boundedness for some multilinear operators generated by singular integral operators and Lipschitz functions on some Hardy and Herz type spaces.
COMMUTATORS WITH REISZ POTENTIALS IN ONE AND SEVERAL PARAMETERS
, 2005
"... Let Mb be the operator of pointwise multiplication by b, that is Mb f = bf. Set [A, B] = AB−BA. The Reisz potentials are the operators Rα f(x) = f(x − y) dy y  α, 0 < α < 1. They map Lp ↦ → Lq, for 1 − α + 1 ..."
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Cited by 1 (0 self)
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Let Mb be the operator of pointwise multiplication by b, that is Mb f = bf. Set [A, B] = AB−BA. The Reisz potentials are the operators Rα f(x) = f(x − y) dy y  α, 0 < α < 1. They map Lp ↦ → Lq, for 1 − α + 1
Weighted continuity of multilinear Marcinkiewicz operators for the extreme cases of p
 Commun. Korean Math. Soc
"... Abstract. In this paper, the continuity of multilinear Marcinkiewicz operators on certain Hardy and Herz–Hardy spaces is obtained. ..."
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Abstract. In this paper, the continuity of multilinear Marcinkiewicz operators on certain Hardy and Herz–Hardy spaces is obtained.
Hardy Space Estimate for the Product of Singular Integrals To the memory of Akihito Uchiyama
"... Abstract. Hp estimate for the multilinear operators which are finite sums of pointwise products of singular integrals and fractional integrals is given. An application to Sobolev space and some examples are also given. 1 ..."
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Abstract. Hp estimate for the multilinear operators which are finite sums of pointwise products of singular integrals and fractional integrals is given. An application to Sobolev space and some examples are also given. 1
URL: www.emis.de/journals/AFA/ LIPSCHITZ ESTIMATES FOR MULTILINEAR COMMUTATOR OF PSEUDODIFFERENTIAL OPERATORS
"... Abstract. In this paper, we prove the boundedness for some multilinear commutators generated by the pseudodifferential operator and Lipschitz functions. 1. ..."
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Abstract. In this paper, we prove the boundedness for some multilinear commutators generated by the pseudodifferential operator and Lipschitz functions. 1.
MaxPlanckInstitut für Mathematik in den Naturwissenschaften Leipzig
, 2012
"... n/pharmonic maps: regularity for the sphere case by ..."
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WEIGHTED BOUNDEDNESS OF MULTILINEAR LITTLEWOOD{PALEY OPERATORS FOR THE EXTREME CASES OF p
"... Abstract: In this paper, we prove the boundedness of multilinear Littlewood{Paley operators for the extreme cases of p. 1 { Preliminaries and results Throughout this paper, Q will denote a cube of Rn with sides parallel to the axes. For a cube Q and a locally integral function f on Rn, denote that f ..."
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Abstract: In this paper, we prove the boundedness of multilinear Littlewood{Paley operators for the extreme cases of p. 1 { Preliminaries and results Throughout this paper, Q will denote a cube of Rn with sides parallel to the axes. For a cube Q and a locally integral function f on Rn, denote that f(Q) = R Q f(x)dx, fQ = jQj¡1 R Q f(x)dx and f #(x) = sup x2Q jQj¡1 RQ jf(y)¡fQjdy. For a weight functions w 2 A1(see[10]), f is said to belong to BMO(w) if f # 2 L1(w) and de¯ne that kfkBMO(w) = kf#kL1(w); If w = 1, we denote that BMO(Rn) = BMO(w). Also, we give the concepts of atom and weighted H1 space. A function a is called a H1(w) atom if there exists a cube Q such that a is supported on Q, kakL1(w) · w(Q)¡1 and R a(x)dx = 0. It is well known that, for w 2 A1, the weighted Hardy space H1(w) has the atomic decomposition characterization (see[2]). In this paper, we will consider a class of multilinear operators related to Littlewood{Paley operators, whose de¯nition are the following.