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

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Matematicheskie Zametki, 2019, Volume 106, Issue 4, paper published in the English version journal (Mi mzm12586)

This article is cited in 9 scientific papers (total in 9 papers)

Papers published in the English version of the journal

Fractional Smoothness in

L^{p}

$L^p$ with Dunkl Weight and Its Applications

D. V. Gorbachev, V. I. Ivanov

Tula State University, Tula, 300012 Russia

Citations (9)

Abstract: We define a fractional power of the Dunkl Laplacian, a fractional modulus of smoothness, and a fractional

K

$K$ -functional on

L^{p}

$L^p$ -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

$K$ -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.

Received: 13.03.2019

English version:
Mathematical Notes, 2019, Volume 106, Issue 4, Pages 537–561
DOI: https://doi.org/10.1134/S0001434619090232

Bibliographic databases:

Document Type: Article

Language: English

Citation: D. V. Gorbachev, V. I. Ivanov, “Fractional Smoothness in

L^{p}

$L^p$ with Dunkl Weight and Its Applications”, Math. Notes, 106:4 (2019), 537–561

Citation in format AMSBIB

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\by D.~V.~Gorbachev, V.~I.~Ivanov

\paper Fractional Smoothness in

$L^p$

with Dunkl Weight

and Its Applications

\jour Math. Notes

\yr 2019

\vol 106

\issue 4

\pages 537--561

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\crossref{https://doi.org/10.1134/S0001434619090232}

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Linking options:

https://www.mathnet.ru/eng/mzm12586

This publication is cited in the following 9 articles:

V. I. Ivanov, “Generalized one-dimensional Dunkl transform in direct problems of approximation theory”, Math. Notes, 116:2 (2024), 265–278
V. I. Ivanov, “Obobschennoe preobrazovanie Danklya na pryamoi v obratnykh zadachakh teorii priblizhenii”, Chebyshevskii sb., 25:2 (2024), 67–81
O. L. Vinogradov, “Sharp Bernstein-type inequalities for Fourier-Dunkl multipliers”, Sb. Math., 214:1 (2023), 1–27
E. S. Bhaya, E. A. Hessen, A. H. Ibrahim, “Dunkl weigted approxmation of functiones”, Physical Mesomechanics of Condensed Matter: Physical Principles of Multiscale Structure Formation and the Mechanisms of Nonlinear Behavior: MESO 2022, AIP Conf. Proc., 2899, 2023, 050034
D. V. Gorbachev, “Bernstein Inequality in $L^p$ on the Line with Power Weight for $p>0$ ”, Math. Notes, 111:2 (2022), 308–311
A. Velicu, N. Yessirkegenov, “Rellich, Gagliardo-Nirenberg, Trudinger and Caffarelli-Kohn-Nirenberg inequalities for Dunkl operators and applications”, Isr. J. Math., 247:2 (2022), 741–782
D. V. Gorbachev, “Tochnye neravenstva Bernshteina — Nikolskogo dlya polinomov i tselykh funktsii eksponentsialnogo tipa”, Chebyshevskii sb., 22:5 (2021), 58–110
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
D. V. Gorbachev, V. I. Ivanov, “Nikol'skii–Bernstein Constants for Entire Functions of Exponential Spherical Type in Weighted Spaces”, Proc. Steklov Inst. Math. (Suppl.), 309:1 (2020), S24–S35

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

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