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Mat. Zametki, 2019, Volume 106, Issue 4, paper published in the English version journal (Mi mz12586)  

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

Papers published in the English version of the journal

Fractional Smoothness in $L^p$ with Dunkl Weight and Its Applications

D. V. Gorbachev, V. I. Ivanov

Tula State University, Tula, 300012 Russia

Abstract: We define a fractional power of the Dunkl Laplacian, a fractional modulus of smoothness, and a fractional $K$-functional on $L^p$-spaces with Dunkl weight. As an application, we extend our previous results and prove direct and inverse theorems of approximation theory and some inequalities for entire functions of spherical exponential type in the fractional setting.

Keywords: Dunkl transform, generalized translation operator, convolution, Dunkl Laplacian, modulus of smoothness, $K$-functional.

Funding Agency Grant Number
Russian Science Foundation 18-11-00199
This work was supported by the Russian Science Foundation under grant 18-11-00199 and performed at Tula State University.



English version:
Mathematical Notes, 2019, 106:4, 537–561

Bibliographic databases:

Received: 13.03.2019
Language:

Citation: D. V. Gorbachev, V. I. Ivanov, “Fractional Smoothness in <nobr>$L^p$</nobr> with Dunkl Weight and Its Applications”, Math. Notes, 106:4 (2019), 537–561

Citation in format AMSBIB
\Bibitem{GorIva19}
\by D.~V.~Gorbachev, V.~I.~Ivanov
\paper Fractional Smoothness in
<nobr>$L^p$</nobr>
with Dunkl Weight
and Its Applications
\jour Math. Notes
\yr 2019
\vol 106
\issue 4
\pages 537--561
\mathnet{http://mi.mathnet.ru/mz12586}
\crossref{https://doi.org/10.1134/S0001434619090232}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=4028874}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000492034300023}
\elib{https://elibrary.ru/item.asp?id=41704553}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85074126952}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V D. 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
  • Математические заметки Mathematical Notes
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