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arXiv · 2006.01126

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

Aleksandr Rotkevich
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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 $\sum\limits_{k=1}^{\infty}2^{2lk}\left\lvert f(z)-P_{2^k}(z) \right\rvert^2\in L^p(\partial\Omega).$

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Aleksandr Rotkevich. 2020-05-30. Constructive description of Hardy-Sobolev spaces in strictly pseudoconvex domains with minimal smoothness. https://arxiv.org/abs/2006.01126

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