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Fundam. Prikl. Mat., 1995, Volume 1, Issue 3, Pages 753–766 (Mi fpm101)  

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

On Jackson inequality in $L_p(\mathbb T^d)$

A. V. Rozhdestvenskii


Abstract: The author proved some necessary and sufficient conditions on a finite set of $d$–dimensional vectors $\{\alpha_l\}$, when Jackson–Youdin inequality for the approximation of periodic function $f$ by trigonometric polynomials:
$$ E_{n-1}(f)_q\le A\cdot n^{-r +(d/p-d/q)_+}\cdot \max\limits_{l}\|\Delta_{2\pi\alpha_l/n}^m f^{(r)}\|_p, $$
where $A>0$ is independent of $f$ and $n$, holds. A criterion of solvability of the homological equation
$$ f(x)-\frac{1}{(2\pi)^d}\int f(t)dt=\varphi(x+2\pi\alpha)-\varphi(x)\qquada.e. x $$
on the sets of functions $\{f\colon f^{(r)}\in L_p(\mathbb T^d)\}$ is obtained.

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Received: 01.02.1995

Citation: A. V. Rozhdestvenskii, “On Jackson inequality in $L_p(\mathbb T^d)$”, Fundam. Prikl. Mat., 1:3 (1995), 753–766

Citation in format AMSBIB
\Bibitem{Roz95}
\by A.~V.~Rozhdestvenskii
\paper On Jackson inequality in $L_p(\mathbb T^d)$
\jour Fundam. Prikl. Mat.
\yr 1995
\vol 1
\issue 3
\pages 753--766
\mathnet{http://mi.mathnet.ru/fpm101}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1788554}
\zmath{https://zbmath.org/?q=an:0865.42002}


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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. A. V. Rozhdestvenskii, “On absolutely continuous weakly mixing cocycles over irrational rotations”, Sb. Math., 194:5 (2003), 775–792  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Фундаментальная и прикладная математика
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