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- W2953209417 abstract "We define local Hardy spaces of differential forms $h^p_{mathcal D}(wedge T^*M)$ for all $pin[1,infty]$ that are adapted to a class of first order differential operators $mathcal D$ on a complete Riemannian manifold $M$ with at most exponential volume growth. In particular, if $D$ is the Hodge--Dirac operator on $M$ and $Delta=D^2$ is the Hodge--Laplacian, then the local geometric Riesz transform ${D(Delta+aI)^{-{1}/{2}}}$ has a bounded extension to $h^p_D$ for all $pin[1,infty]$, provided that $a>0$ is large enough compared to the exponential growth of $M$. A characterisation of $h^1_{mathcal D}$ in terms of local molecules is also obtained. These results can be viewed as the localisation of those for the Hardy spaces of differential forms $H^p_D(wedge T^*M)$ introduced by Auscher, McIntosh and Russ." @default.
- W2953209417 created "2019-06-27" @default.
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- W2953209417 date "2010-03-31" @default.
- W2953209417 modified "2023-09-23" @default.
- W2953209417 title "Local Hardy Spaces of Differential Forms on Riemannian Manifolds" @default.
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