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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 23 (6 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
COMMUTATORS WITH REISZ POTENTIALS IN ONE AND SEVERAL PARAMETERS
, 2006
"... Abstract. 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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Abstract. 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 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 1 (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.
Printed in India Multilinear integral operators and mean oscillation
, 2003
"... Abstract. In this paper, the boundedness properties for some multilinear operators related to certain integral operators from Lebesgue spaces to Orlicz spaces are obtained. The operators include Calderón–Zygmund singular integral operator, fractional integral operator, Littlewood–Paley operator and ..."
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Abstract. In this paper, the boundedness properties for some multilinear operators related to certain integral operators from Lebesgue spaces to Orlicz spaces are obtained. The operators include Calderón–Zygmund singular integral operator, fractional integral operator, Littlewood–Paley operator and Marcinkiewicz operator. Keywords. Multilinear operator; Calderón–Zygmund operators; fractional integral operator; Littlewood–Paley operator; Marcinkiewicz operator; BMO space; Orlicz space.
s.reisz
, 2005
"... Abstract. 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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Abstract. 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
Characterizations of BMO Associated with Gauss Measures via Commutators of Local Fractional Integrals
, 903
"... Abstract Let dγ(x) ≡ π−n/2e−x2dx for all x ∈ Rn be the Gauss measure on Rn. In this paper, the authors establish the characterizations of the space BMO(γ) of Mauceri and Meda via commutators of either local fractional integral operators or local fractional maximal operators. To this end, the auth ..."
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Abstract Let dγ(x) ≡ π−n/2e−x2dx for all x ∈ Rn be the Gauss measure on Rn. In this paper, the authors establish the characterizations of the space BMO(γ) of Mauceri and Meda via commutators of either local fractional integral operators or local fractional maximal operators. To this end, the authors first prove that such a local fractional integral operator of order β is bounded from Lp (γ) to Lp/(1−pβ) (γ), or from the Hardy space H1 (γ) of Mauceri and Meda to L1/(1−β) (γ) or from L1/β (γ) to BMO(γ), where β ∈ (0, 1) and p ∈ (1, 1/β). 1
© Hindawi Publishing Corp. BOUNDEDNESS OF MULTILINEAR OPERATORS ON TRIEBELLIZORKIN SPACES
, 2003
"... The purpose of this paper is to study the boundedness in the context of TriebelLizorkin spaces for some multilinear operators related to certain convolution operators. The operators include LittlewoodPaley operator, Marcinkiewicz integral, and BochnerRiesz operator. 2000 Mathematics Subject Class ..."
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The purpose of this paper is to study the boundedness in the context of TriebelLizorkin spaces for some multilinear operators related to certain convolution operators. The operators include LittlewoodPaley operator, Marcinkiewicz integral, and BochnerRiesz operator. 2000 Mathematics Subject Classification: 42B20, 42B25. 1. Introduction. Let T be a CalderonZygmund operator. A wellknown result of Coifman et al. [6] states that the commutator [b,T] = T(bf) − bTf (where b ∈ BMO) is bounded on L p (R n) for 1 <p<∞; Chanillo [1] proves a similar result when T is replaced by the fractional integral operator. In [7, 9], Janson and Paluszyński extend these results to the TriebelLizorkin spaces and the case b ∈ Lipβ (where Lipβ is the