Riesz transform on manifolds with quadratic curvature decay.

Gilles Carron (1)

1 Géométrie et analyse globale

We investigate the $L^p$-boundness of the Riesz transform on Riemannian manifolds whose Ricci curvature has quadratic decay. Two criteria for the $L^p$-unboundness of the Riesz transform are given. We recover known results about manifolds that are Euclidean or conical at infinity.

Mots clés: Riesz transform; harmonic forms; heat kernel

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

Gilles Carron. Riesz transform on manifolds with quadratic curvature decay.. Revista Matemática Iberoamericana, 2017, 33 (3), pp.749-788. ⟨10.4171/RMI/954⟩. ⟨hal-00965293v2⟩