Hardy spaces and divergence operators on strongly Lipschitz domains in $R^n$
| dc.creator | Auscher, P. | |
| dc.creator | Russ, E. | |
| dc.date | 2002-01-30 | |
| dc.date.accessioned | 2026-07-07T04:46:12Z | |
| dc.date.available | 2026-07-07T04:46:12Z | |
| dc.description | Let $Ω$ be a strongly Lipschitz domain of $\reel^n$. Consider an elliptic second order divergence operator $L$ (including a boundary condition on $\partialΩ$) and define a Hardy space by imposing the non-tangential maximal function of the extension of a function $f$ via the Poisson semigroup for $L$ to be in$L^1$. Under suitable assumptions on $L$, we identify this maximal Hardy space with atomic Hardy spaces, namely with $H^1(\reel^n)$ if $Ω=\reel^n$, $H^{1}_{r}(Ω)$ under the Dirichlet boundary condition, and $H^{1}_{z}(Ω)$ under the Neumann boundary condition. In particular, we obtain a new proof of the atomic decomposition for $H^{1}_{z}(Ω)$. A version for local Hardy spaces is also given. We also present an overview of the theory of Hardy spaces and BMO spaces on Lipschitz domains with proofs. | |
| dc.description | submitted | |
| dc.identifier | https://arxiv.org/abs/math/0201301 | |
| dc.identifier | http://arxiv.org/abs/math/0201301 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63237 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 42B30, 42B25 | |
| dc.title | Hardy spaces and divergence operators on strongly Lipschitz domains in $R^n$ | |
| dc.type | text |