Jackson theorems in Hardy spaces and approximation by Riesz means (Q1110762)

\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.