Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part IV: Riesz transforms on manifolds and weights

Pascal Auscher (1) , José Maria Martell (2)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 IMFF - Instituto de Matematicas y Fisica Fundamental

This is the fourth article of our series. Here, we apply the results of \cite{AM1} to study weighted norm inequalities for the Riesz transform of the Laplace-Beltrami operator on Riemannian manifolds and of subelliptic sum of squares on Lie groups, under the doubling volume property and Poincaré inequalities.

Mots clés: Riemannian manifolds; Riesz transforms; Muckenhoupt weights; Poincaré inequalities

Domaines: Géométrie différentielle [math.DG]; Analyse classique [math.CA]; Equations aux dérivées partielles [math.AP]

Pascal Auscher, José Maria Martell. Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part IV: Riesz transforms on manifolds and weights. 2006. ⟨hal-00021879v1⟩