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Mat. Sb., 2012, Volume 203, Number 8, Pages 79–96 (Mi msb7888)  

This article is cited in 1 scientific paper (total in 1 paper)

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

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.

DOI: https://doi.org/10.4213/sm7888

Full text: PDF file (613 kB)
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English version:
Sbornik: Mathematics, 2012, 203:8, 1151–1168

Bibliographic databases:

UDC: 517.551
MSC: Primary 41A35, 42B30; Secondary 42B15
Received: 15.05.2011 and 27.12.2011

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yu. Kolomoitsev, “On moduli of smoothness and averaged differences of fractional order”, Fract. Calc. Appl. Anal., 20:4 (2017), 988–1009  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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