论文标题
耐力空间的扩展域
Extension domains for Hardy spaces
论文作者
论文摘要
我们表明，当且仅当它满足某个几何条件时，只有适当的打开子集$ω\ subset \ subset \ mathbb {r}^n $是$ h^p $（$ 0 <p \ le1 $）的扩展域。当$ n（\ frac {1} {p} -1）\ in \ mathbb {n} $此条件等于$ω^c $的全球马尔可夫条件，$ p = 1 $，当$ n（\ n（\ frac {\ frac {1}} {1} {1} {p} -1} {p} -1）子集是$ h^p $的扩展域。结果表明，在每种情况下都存在线性扩展运算符。我们应用结果来研究$ bmo（\ mathbb {r}^n）$的一些补充子空间。
We show that a proper open subset $Ω\subset \mathbb{R}^n$ is an extension domain for $H^p$ ($0<p\le1$), if and only if it satisfies a certain geometric condition. When $n(\frac{1}{p}-1)\in \mathbb{N}$ this condition is equivalent to the global Markov condition for $Ω^c$, for $p=1$ it is stronger, and when $n(\frac{1}{p}-1)\notin \mathbb{N}\cup \{0\}$ every proper open subset is an extension domain for $H^p$. It is shown that in each case a linear extension operator exists. We apply our results to study some complemented subspaces of $BMO(\mathbb{R}^n)$.
