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Local Hardy Spaces of Differential Forms on Riemannian Manifolds

Carbonaro, Andrea; McIntosh, Alan; Morris, Andrew J.


We define local Hardy spaces of differential forms hDᴾ(∧T∗M) for all p∈[1,∞] that are adapted to a class of first-order differential operators D on a complete Riemannian manifold M with at most exponential volume growth. In particular, if D is the Hodge–Dirac operator on M and Δ=D² is the Hodge–Laplacian, then the local geometric Riesz transform D(Δ+aI)⁻¹/² has a bounded extension to hDᴾ for all p∈[1,∞], provided that a>0 is large enough compared to the exponential growth of M. A...[Show more]

CollectionsANU Research Publications
Date published: 2011-05-24
Type: Journal article
Source: Journal of Geometric Analysis
DOI: 10.1007/s12220-011-9240-x


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