Hardy spaces of differential forms on Riemannian manifolds

2006/11/11 by Pascal Auscher, Auscher, Pascal, Alan Mcintosh +3
Mathematics · #42B30 #47A60 #47F05 #58J05 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:42B30 #msc:47A60 #msc:47F05 #msc:58J05

paper · pdf · doi:10.48550/arxiv.math/0611334

arxiv created 2006/11/14 · arxiv updated 2009/12/01

Abstract

Let M be a complete connected Riemannian manifold. Assuming that the Riemannian measure is doubling, we define Hardy spaces H^p of differential forms on M and give various characterizations of them, including an atomic decomposition. As a consequence, we derive the H^p-boundedness for Riesz transforms on M, generalizing previously known results. Further applications, in particular to H^∞ functional calculus and Hodge decomposition, are given.

Related

• Local Hardy Spaces of Differential Forms on Riemannian Manifolds
• Hardy spaces and heat kernel regularity
• Local Riesz transform and local Hardy spaces on Riemannian manifolds with bounded geometry
• Atomic decomposition of Hardy type spaces on certain noncompact manifolds
• Riesz transforms on non-compact manifolds