Revista Matemática Iberoamericana
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Published online: 2017-10-02
Riesz transform on manifolds with quadratic curvature decayGilles Carron (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. Iberoam. 33 (2017), 749-788. doi: 10.4171/RMI/954