论文标题
严格的伪convex域中的耐强 - 贝贝尔空间的建设性描述，平滑度最低
Constructive description of Hardy-Sobolev spaces in strictly pseudoconvex domains with minimal smoothness
论文作者
论文摘要
令$ω\ subset \ mathbb {c}^n $是一个严格的pseudoconvex runge域，具有$ c^2 $ - s-smooth定义功能，$ l \ in \ mathbb {n}，$ $ $ $ p \ in（in（1，\ infty）。如果存在多项式上的顺序$ p_n $ $ n $，以便$ \ sum \ limits_ {k = 1}^{\ infty}^{\ infty} 2^{2lk} \ left \ left \ lvert f（z）-p_p_ {z）-p_ {2^k}（z）\ rvert \ rvert \ rvert \ rvert \ rvert \ rvert \ rvert \ rvert \ rvert^2 p（$）
Let $Ω\subset\mathbb{C}^n$ be a strictly pseudoconvex Runge domain with $C^2$-smooth defining function, $l\in\mathbb{N},$ $p\in(1,\infty).$ We prove that the holomorphic function $f$ has derivatives of order $l$ in $H^p(Ω)$ if and only if there exists a sequence on polynomials $P_n$ of degree $n$ such that $\sum\limits_{k=1}^{\infty}2^{2lk}\left\lvert f(z)-P_{2^k}(z) \right\rvert^2\in L^p(\partialΩ).$
