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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 61 (15 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
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 17 (7 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 12 (5 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)
*Correspondence to:
"... Tonic and phasic electroencephalographic dynamics during continuous compensatory tracking ..."
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Cited by 6 (1 self)
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Tonic and phasic electroencephalographic dynamics during continuous compensatory tracking
LOCAL CUT POINTS AND METRIC MEASURE SPACES WITH RICCI CURVATURE BOUNDED BELOW
, 2006
"... Abstract. A local cut point is by definition a point that disconnects its sufficiently small neighborhood. We show that there exists an upper bound for the degree of a local cut point in a metric measure space satisfying the generalized Bishop–Gromov inequality. As a corollary, we obtain an upper bo ..."
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Cited by 4 (0 self)
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Abstract. A local cut point is by definition a point that disconnects its sufficiently small neighborhood. We show that there exists an upper bound for the degree of a local cut point in a metric measure space satisfying the generalized Bishop–Gromov inequality. As a corollary, we obtain an upper bound for the number of ends of such a space. We also obtain some obstruction conditions for the existence of a local cut point in a metric measure space satisfying the Bishop–Gromov inequality or the Poincaré inequality. For example, the measured Gromov–Hausdorff limits of Riemannian manifolds with a lower Ricci curvature bound satisfy these two inequalities. 1.
Michigan Math. J. 53 (2005) CarlesonType Estimates for pHarmonic Functions and the Conformal Martin Boundary of John Domains in Metric Measure Spaces
"... In the study of the local Fatou theorem for harmonic functions, Carleson [Ca] proved the following crucial estimate for positive harmonic functions, now referred to as the Carleson estimate. Given a bounded Lipschitz domain D in the Euclidean space Rn, there exist constants K,C> 1, depending onl ..."
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In the study of the local Fatou theorem for harmonic functions, Carleson [Ca] proved the following crucial estimate for positive harmonic functions, now referred to as the Carleson estimate. Given a bounded Lipschitz domain D in the Euclidean space Rn, there exist constants K,C> 1, depending only on D, with
MOSER'S METHOD FOR MINIMIZERS ON METRIC MEASURE SPACES
"... Niko Marola: Moser's method for minimizers on metric measure spaces; Helsinki ..."
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Niko Marola: Moser's method for minimizers on metric measure spaces; Helsinki
the Conformal Martin boundary of John domains in
"... Carleson type estimates for pharmonic functions and ..."
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Hölder estimates of pharmonic extension operators
"... It is now a wellknown fact that for 1 < p < ∞ the pharmonic functions on domains in metric measure spaces equipped with a doubling measure supporting a (1, p)Poincare ́ inequality are locally Hölder continuous. In this note we provide a characterization of domains in such metric spaces for ..."
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It is now a wellknown fact that for 1 < p < ∞ the pharmonic functions on domains in metric measure spaces equipped with a doubling measure supporting a (1, p)Poincare ́ inequality are locally Hölder continuous. In this note we provide a characterization of domains in such metric spaces for which pharmonic extensions of Hölder continuous boundary data are globally Hölder continuous. We also provide a link between this regularity property of the domain and the uniform pfatness of the complement of the domain.