تقرير
Potential maps, Hardy spaces, and tent spaces on special Lipschitz domains
| العنوان: | Potential maps, Hardy spaces, and tent spaces on special Lipschitz domains |
|---|---|
| المؤلفون: | Costabel, Martin, McIntosh, Alan, Taggart, Robert J. |
| سنة النشر: | 2010 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, Mathematics - Differential Geometry, Mathematics - Functional Analysis, 35B65, 35C15, 58J10, 47G10, 42B30 |
| الوصف: | Suppose that $\Omega$ is the open region in $\mathbb{R}^n$ above a Lipschitz graph and let $d$ denote the exterior derivative on $\mathbb{R}^n$. We construct a convolution operator $T $ which preserves support in $\bar{\Omega$}, 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 $\bar\Omega$. Thus if $f$ is exact and supported in $\bar\Omega$, then there is a potential $u$, given by $u=Tf$, of optimal regularity and supported in $\bar\Omega$, such that $du=f$. This has implications for the regularity in homogeneous function spaces of the de Rham complex on $\Omega$ with or without boundary conditions. The operator $T$ is used to obtain an atomic characterisation of Hardy spaces $H^p$ of exact forms with support in $\bar\Omega$ when $n/(n+1) |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1006.0562 |
| رقم الأكسشن: | edsarx.1006.0562 |
| قاعدة البيانات: | arXiv |
كن أول من يترك تعليقا!