Constructive description of Hardy-Sobolev spaces in $\mathbb{C}^n$

TL;DR

This paper characterizes Hardy-Sobolev spaces in convex domains of or ocusing on polynomial approximations and using pseudoanalytical continuation methods.

Contribution

It provides a new characterization of Hardy-Sobolev spaces in convex domains via polynomial approximations and pseudoanalytical continuation.

Findings

Characterization of Hardy-Sobolev spaces in convex domains.

Use of pseudoanalytical continuation for space description.

Advancement in polynomial approximation techniques.

Abstract

In this paper we study the polynomial approximations in Hardy-Sobolev spaces on for convex domains. We use the method of pseudoanalytical continuation to obtain the characterization of these spaces in terms of polynomial approximations.