Results 1 
7 of
7
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 ..."
Abstract

Cited by 21 (7 self)
 Add to MetaCart
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. ..."
Abstract

Cited by 7 (2 self)
 Add to MetaCart
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) ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
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)
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 ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
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.
the Conformal Martin boundary of John domains in
"... Carleson type estimates for pharmonic functions and ..."
MOSER'S METHOD FOR MINIMIZERS ON METRIC MEASURE SPACES
"... Niko Marola: Moser's method for minimizers on metric measure spaces; Helsinki ..."
Abstract
 Add to MetaCart
Niko Marola: Moser's method for minimizers on metric measure spaces; Helsinki