| Date: |
2013 |
| Abstract: |
Suppose that Ω is the open region in ℝn above a Lipschitz graph and let d denote the exterior derivative on ℝn. We construct a convolution operator T which preserves support in Ω is smoothing of order 1 on the homogeneous function spaces, and is a potential map in the sense that dT is the identity on spaces of exact forms with support in Ω. Thus if f is exact and supported in Ω then there is a potential u, given by u = T f, of optimal regularity and supported in Ω, such that du = f. This has implications for the regularity in homogeneous function spaces of the de Rham complex on Ω with or without boundary conditions. The operator T is used to obtain an atomic characterisation of Hardy spaces Hp of exact forms with support in Ω when n/(n + 1) < p ≤ 1. This is done via an atomic decomposition of functions in the tent spaces Tp(ℝn _ ℝ+) with support in a tent T(Ω) as a sum of atoms with support away from the boundary of Ω . This new decomposition of tent spaces is useful, even for scalar valued functions. |
| Rights: |
Tots els drets reservats.  |
| Language: |
Anglès |
| Document: |
Article ; recerca ; Versió publicada |
| Subject: |
Exterior derivative ;
Dierential forms ;
Lipschitz domain ;
Potential map ;
Sobolev space ;
Hardy space ;
Tent space |
| Published in: |
Publicacions matemàtiques, Vol. 57, Núm. 2 (2013) , p. 295-331, ISSN 2014-4350 |
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