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Matematicheskie Zametki, 2007, Volume 82, Issue 3, Pages 426–440
DOI: https://doi.org/10.4213/mzm3854
(Mi mzm3854)
 

This article is cited in 8 scientific papers (total in 8 papers)

Comparison of Linear Differential Operators

R. M. Trigub

Donetsk National University
Full-text PDF (515 kB) Citations (8)
References:
Abstract: In this paper, we study the question of the existence of the inequality
$$ \|Q(D)f\|_{L_q}\le\gamma_0\|P(D)f\|_{L_p}, $$
where $P$ and $Q$ are algebraic polynomials, $D=d/dx$, and $\gamma_0$ is independent of the function $f$. We obtain criteria (necessary and simultaneously sufficient conditions) for the existence of such inequalities for functions on the circle, on the whole line, and on the semiaxis. Besides, for the semiaxis, we obtain an inequality for $q=\infty$ and any $p\ge1$ with the smallest constant $\gamma_0$.
Keywords: linear differential operator, algebraic polynomial, Kolmogorov multiplicative inequality, Fourier series, Schoenberg spline, Hölder's inequality, Minkowski's inequality.
Received: 27.02.2006
Revised: 16.10.2006
English version:
Mathematical Notes, 2007, Volume 82, Issue 3, Pages 380–394
DOI: https://doi.org/10.1134/S0001434607090118
Bibliographic databases:
UDC: 517.5
Language: Russian
Citation: R. M. Trigub, “Comparison of Linear Differential Operators”, Mat. Zametki, 82:3 (2007), 426–440; Math. Notes, 82:3 (2007), 380–394
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm3854
  • https://www.mathnet.ru/eng/mzm/v82/i3/p426
  • This publication is cited in the following 8 articles:
    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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    Full-text PDF :334
    References:65
    First page:7
     
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