Jackson theorems in Hardy spaces and approximation by Riesz means
type: Item
instance of: scholarly article
title: Jackson theorems in Hardy spaces and approximation by Riesz means
zbMATH Open document ID: 0657.42024
DOI: 10.1016/0021-9045(87)90101-8
author: Leonardo Colzani
published in: Journal of Approximation Theory
publication date: 1987-01-01T00:00:00Z
review text: \textit{E. A. Storozhenko} [Izv. Akad. Nauk SSSR Ser. Mat. 44, 946-962 (1980; Zbl 0455.42002)] considered theorems of Jackson type in the classical Hardy spaces on the unit disc of the complex plane, \(H^ p\), \(0<p<1\). In the present paper the author is concerned with an extension of Jackson's theorem to other Hardy spaces of several variables. His main interest is in approximating distributions in \(H^ p({\mathbb{R}}^ N)\), \(0<p<+\infty\) by means of entire functions of finite exponential type (the analog in \({\mathbb{R}}^ N\) of the trigonometric polynomials). As the author says in the introduction, he is able to prove a theorem of Jackson type in \(H^ p({\mathbb{R}}^ N)\) only after having established an analog of this theorem for Hardy spaces on polydiscs and on some tube domains of \({\mathbb{C}}^ N\). Here the contents: 1. Hardy spaces of several variables. 2. The Jackson theorem for the polydisc. 3. The Jackson theorem for poly- half-space. 4. The Jackson theorem for \({\mathbb{R}}^ N\). 5. Approximation by Riesz means.
Mathematics Subject Classification ID: 42C10
Mathematics Subject Classification ID: 42A05
zbMATH DE Number: 4073690
zbMATH Keywords: Hardy spaces
zbMATH Keywords: Jackson's theorem
zbMATH Keywords: polydisc
zbMATH Keywords: poly-half-space
zbMATH Keywords: Riesz means
MaRDI profile type: Publication
full work available at URL: 0021-9045(87)90101-8
OpenAlex ID: W2009782102
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description: scientific article; zbMATH DE number 4073690