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Matematicheskie Zametki, 2014, Volume 95, Issue 3, Pages 433–444
DOI: https://doi.org/10.4213/mzm9196 (Mi mzm9196) 		 
This article is cited in 1 scientific paper (total in 1 paper)

$L_p$-Inequalities for Differences and Derivatives of Positive Order for Functions with Spectrum in the Ball or Spherical Layer

N. L. Kudryavtsev

M. V. Lomonosov Moscow State University
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DOI: https://doi.org/10.4213/mzm9196
Abstract: We prove inequalities of Riesz, Bernstein, and Bohr–Favard type in the metric of the spaces $L_p$, $0<p<\infty$, for functions whose spectrum is contained in a closed ball or a closed spherical layer. As an application, a discrete description of Lizorkin–Triebel spaces in terms of coordinate differences of positive order is given.
Keywords: $L_p$-inequality, Riesz-type inequality, Bernstein-type inequality, Bohr–Favard type inequality, $L_p$ space, Lizorkin–Triebel space, functions whose spectrum is contained in a closed ball or a closed spherical layer, Fourier transform, Young's inequality.
Received: 12.07.2011
Revised: 10.06.2013
English version:
Mathematical Notes, 2014, Volume 95, Issue 3, Pages 388–398
DOI: https://doi.org/10.1134/S0001434614030109
Bibliographic databases:
Document Type: Article
UDC: 517.518.2
Language: Russian
Citation: N. L. Kudryavtsev, “$L_p$-Inequalities for Differences and Derivatives of Positive Order for Functions with Spectrum in the Ball or Spherical Layer”, Mat. Zametki, 95:3 (2014), 433–444; Math. Notes, 95:3 (2014), 388–398
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
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