Constructive description of Hardy-Sobolev spaces in strictly pseudoconvex domains with minimal smoothness

Abstract

Let $\Omega \subset {\mathbb{C}}^n$ 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 $H^p(\Omega )$ if and only if there exists a sequence on polynomials $P_n$ of degree $n$ such that $\sum _{k=1}^{\infty }{2}^{2lk}{\left|f(z)-P_{2^k}(z)\right|}^2\in L^p(\partial \Omega ).$

arXiv admin note: text overlap with arXiv:1907.01584