This article is cited in 5 papers

Approximation properties of generalized Bochner-Riesz means in the Hardy spaces $H_p$, $0<p\le 1$

Yu. S. Kolomoitsev<sup>ab

a</sup> Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences, Donetsk
^b Donetsk National University

Abstract: A test for the convergence of the generalized spherical and $\ell_1$ Bochner-Riesz means in the Hardy spaces $H_p(D^n)$, $0<p\le 1$, is obtained, where $D^n$ is the unit polydisc. Precise orders of the approximation of functions by the generalized $\ell_q$ Bochner-Riesz means in terms of the $K$-functional and special moduli of smoothness are found.
Bibliography: 31 titles.

Keywords: Hardy spaces in a polydisc, generalized Bochner-Riesz means, $K$-functional, moduli of smoothness, Bernstein-type inequalities.

UDC: 517.551

MSC: Primary 41A35, 42B30; Secondary 42B15

Received: 15.05.2011 and 27.12.2011

DOI: 10.4213/sm7888

 English version: Sbornik: Mathematics, 2012, 203:8, 1151–1168

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