Results 1  10
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19
Gaussian heat kernel upper bounds via the PhragmnLindelf theorem
 Proc. Lond. Math. Soc
"... Abstract. We prove that in presence of L 2 Gaussian estimates, socalled DaviesGaffney estimates, ondiagonal upper bounds imply precise offdiagonal Gaussian upper bounds for the kernels of analytic families of operators on metric measure spaces. Contents ..."
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Cited by 7 (0 self)
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Abstract. We prove that in presence of L 2 Gaussian estimates, socalled DaviesGaffney estimates, ondiagonal upper bounds imply precise offdiagonal Gaussian upper bounds for the kernels of analytic families of operators on metric measure spaces. Contents
Riesz transform on manifolds and Poincaré inequalities
, 2005
"... We study the validity of the L p inequality for the Riesz transform when p> 2 and of its reverse inequality when p < 2 on complete Riemannian manifolds under the doubling property and some Poincaré inequalities. ..."
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Cited by 6 (2 self)
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We study the validity of the L p inequality for the Riesz transform when p> 2 and of its reverse inequality when p < 2 on complete Riemannian manifolds under the doubling property and some Poincaré inequalities.
Interpolation of Sobolev spaces, LittlewoodPaley inequalities and Riesz transforms on graphs
 PUBLICACIONS MATEMATIQUES
"... Abstract. Let Γ be a graph endowed with a reversible Markov kernel p, and P the associated operator, defined by Pf(x) = ∑ y p(x, y)f(y). Denote by ∇ the discrete gradient. We give necessary and/or sufficient conditions on Γ in order to compare ‖∇f‖ p and ∥ ∥ (I − P) ..."
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Cited by 5 (2 self)
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Abstract. Let Γ be a graph endowed with a reversible Markov kernel p, and P the associated operator, defined by Pf(x) = ∑ y p(x, y)f(y). Denote by ∇ the discrete gradient. We give necessary and/or sufficient conditions on Γ in order to compare ‖∇f‖ p and ∥ ∥ (I − P)
REAL INTERPOLATION OF SOBOLEV SPACES ASSOCIATED TO A Weight
, 2008
"... We study the interpolation property of Sobolev spaces of order 1 denoted by W 1 p,V, arising from Schrödinger operators with positive potential. We show that for 1 ≤ p1 < p < p2 < q0 with p> s0, W 1 p,V is a real interpolation space between W 1 p1,V and W 1 p2,V on some classes of manifolds and Li ..."
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Cited by 4 (2 self)
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We study the interpolation property of Sobolev spaces of order 1 denoted by W 1 p,V, arising from Schrödinger operators with positive potential. We show that for 1 ≤ p1 < p < p2 < q0 with p> s0, W 1 p,V is a real interpolation space between W 1 p1,V and W 1 p2,V on some classes of manifolds and Lie groups. The constants s0, q0 depend on our hypotheses.
Use of abstract Hardy spaces, real interpolation and applications to bilinear operators. submitted, page available at http://fr.arxiv.org/abs/0809.4110
, 2008
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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.
Lp selfimprovement of generalized Poincaré inequalities in spaces of homogeneous type
 J. Funct. Anal
"... Abstract. In this paper we study selfimproving properties in the scale of Lebesgue spaces of generalized Poincaré inequalities in spaces of homogeneous type. In contrast with the classical situation, the oscillations involve approximation of the identities or semigroups whose kernels decay fast eno ..."
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Abstract. In this paper we study selfimproving properties in the scale of Lebesgue spaces of generalized Poincaré inequalities in spaces of homogeneous type. In contrast with the classical situation, the oscillations involve approximation of the identities or semigroups whose kernels decay fast enough and the resulting estimates take into account their lack of localization. The techniques used do not involve any classical Poincaré or SobolevPoincaré inequalities and therefore they can be used in general settings where these estimates do not hold or are unknown. We apply our results to the case of Riemannian manifolds with doubling volume form and assuming Gaussian upper bounds for the heat kernel of the semigroup e −t ∆ with ∆ being the LaplaceBeltrami operator. We obtain generalized Poincaré inequalities with oscillations that involve the semigroup e−t ∆ and with right hand sides containing either ∇ or ∆1/2. 1.
Maximal inequalities for dual sobolev spaces W −1,p and applications to interpolation, submitted, available at http://fr.arxiv.org/abs/0812.3075
, 2008
"... We firstly describe a maximal inequality for dual Sobolev spaces W −1,p. This one corresponds to a “Sobolev version ” of usual properties of the HardyLittlewood maximal operator in Lebesgue spaces. Even in the euclidean space, this one seems to be new and we develop arguments in the general framewo ..."
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We firstly describe a maximal inequality for dual Sobolev spaces W −1,p. This one corresponds to a “Sobolev version ” of usual properties of the HardyLittlewood maximal operator in Lebesgue spaces. Even in the euclidean space, this one seems to be new and we develop arguments in the general framework of Riemannian manifold. Then we present an application to obtain interpolation results for Sobolev
unknown title
, 2004
"... On necessary and sufficient conditions for L pestimates of Riesz transforms associated to elliptic operators on R n and related estimates ..."
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On necessary and sufficient conditions for L pestimates of Riesz transforms associated to elliptic operators on R n and related estimates
Contents
, 2007
"... Abstract. Let L be an elliptic differential operator with bounded measurable coefficients, acting in Bochner spaces L p (R n; X) of Xvalued functions on R n. We characterize Kato’s square root estimates ‖ √ Lu‖p � ‖∇u‖p and the H ∞functional calculus of L in terms of Rboundedness properties of t ..."
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Abstract. Let L be an elliptic differential operator with bounded measurable coefficients, acting in Bochner spaces L p (R n; X) of Xvalued functions on R n. We characterize Kato’s square root estimates ‖ √ Lu‖p � ‖∇u‖p and the H ∞functional calculus of L in terms of Rboundedness properties of the resolvent of L, when X is a Banach function lattice with the UMD property, or a noncommutative L p space. To do so, we develop various vectorvalued analogues of classical objects in Harmonic Analysis, including a maximal function for Bochner spaces. In the special case X = C, we get a new approach to the L p theory of square roots of elliptic operators, as well as an L p version of Carleson’s inequality.