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Sbornik: Mathematics, 2012, Volume 203, Issue 8, Pages 1151–1168
DOI: https://doi.org/10.1070/SM2012v203n08ABEH004258 (Mi sm7888) 		 
This article is cited in 4 scientific papers (total in 4 papers)

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

Yu. S. Kolomoitsevab

a Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences, Donetsk
b Donetsk National University
English version PDF (418 kB) Citations (4)
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DOI: https://doi.org/10.1070/SM2012v203n08ABEH004258
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.
Received: 15.05.2011 and 27.12.2011
Russian version:
Matematicheskii Sbornik, 2012, Volume 203, Number 8, Pages 79–96
DOI: https://doi.org/10.4213/sm7888
Bibliographic databases:
Document Type: Article
UDC: 517.551
MSC: Primary 41A35, 42B30; Secondary 42B15
Language: English
Original paper language: Russian
Citation: Yu. S. Kolomoitsev, “Approximation properties of generalized Bochner-Riesz means in the Hardy spaces $H_p$, $0<p\le 1$”, Mat. Sb., 203:8 (2012), 79–96; Sb. Math., 203:8 (2012), 1151–1168
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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