Revista Matemática Iberoamericana


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Volume 33, Issue 3, 2017, pp. 749–788
DOI: 10.4171/RMI/954

Riesz transform on manifolds with quadratic curvature decay

Gilles Carron[1]

(1) Université de Nantes, France

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

Keywords: Riesz transform, harmonic forms, heat kernel

Carron Gilles: Riesz transform on manifolds with quadratic curvature decay. Rev. Mat. Iberoamericana 33 (2017), 749-788. doi: 10.4171/RMI/954