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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 $L_p(\mathbb R^d)$ 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 $L_p(\mathbb R^d)$, $1\le p<2$, 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 $L_p$, 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 $L_p(\mathbb R^d)$ 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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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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