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Matematicheskie Zametki, 2019, Volume 105, Issue 5, Pages 666–684
DOI: https://doi.org/10.4213/mzm12387 (Mi mzm12387) 		 
This article is cited in 3 scientific papers (total in 3 papers)

A Sharp Jackson Inequality in Lp(Rd) with Dunkl Weight

D. V. Gorbachev, V. I. Ivanov

Tula State University
Full-text PDF (591 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm12387
Abstract: A sharp Jackson inequality in the space Lp(Rd), 1⩽p<2, with Dunkl weight is proved. The best approximation is realized by entire functions of exponential spherical type. The modulus of continuity is defined by means of a generalized shift operator bounded on Lp, which was constructed earlier by the authors. In the case of the unit weight, this operator coincides with the mean-value operator on the sphere.
Keywords: Dunkl transform, best approximation, generalized shift operator, modulus of continuity, Jackson inequality.
Funding agency Grant number
Russian Science Foundation 18-11-00199
This work was supported by the Russian Science Foundation under grant 18-11-00199.
Received: 19.10.2018
English version:
Mathematical Notes, 2019, Volume 105, Issue 5, Pages 657–673
DOI: https://doi.org/10.1134/S0001434619050031
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: D. V. Gorbachev, V. I. Ivanov, “A Sharp Jackson Inequality in Lp(Rd) with Dunkl Weight”, Mat. Zametki, 105:5 (2019), 666–684; Math. Notes, 105:5 (2019), 657–673
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm12387
  • https://www.mathnet.ru/eng/mzm/v105/i5/p666
    • This publication is cited in the following 3 articles:
    1. M. A. Boubatra, “Bernstein-Nikolskii-Stechkin inequality and Jackson's theorem for the index Whittaker transform”, Ann Univ Ferrara, 2023  crossref
    2. I. A. Martyanov, “Konstanta Nikolskogo dlya trigonometricheskikh polinomov s periodicheskim vesom Gegenbauera”, Chebyshevskii sb., 21:1 (2020), 247–258  mathnet  crossref
    3. D. V. Gorbachev, V. I. Ivanov, S. Yu. Tikhonov, “Sharp approximation theorems and Fourier inequalities in the dunkl setting”, J. Approx. Theory, 258 (2020), 105462  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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