V. I. Ivanov, “Direct and converse theorems of the theory of approximation in the metric of $L_p$ for $0<p<1$”, Mat. Zametki, 18:5 (1975), 641–658; Math. Notes, 18:5 (1975), 972

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Matematicheskie Zametki, 1975, Volume 18, Issue 5, Pages 641–658 (Mi mzm7677)

This article is cited in 17 scientific papers (total in 17 papers)

Direct and converse theorems of the theory of approximation in the metric of

$L_p$ for

$0<p<1$

V. I. Ivanov

V. A. Steklov Mathematical Institute, USSR Academy of Sciences

Full-text PDF (944 kB) Citations (17)

Abstract: A direct theorem of the Jackson type and several converse theorems are established for the approximation of periodic functions of period

$2\pi$ by trigonometrical polynomials in the metric of

$L_p$ ,

$0<p<1$ .

Received: 18.06.1975

English version:
Mathematical Notes, 1975, Volume 18, Issue 5, Pages 972–982
DOI: https://doi.org/10.1007/BF01153563

Bibliographic databases:

UDC: 517.51

Language: Russian

Citation: V. I. Ivanov, “Direct and converse theorems of the theory of approximation in the metric of

$L_p$ for

$0<p<1$ ”, Mat. Zametki, 18:5 (1975), 641–658; Math. Notes, 18:5 (1975), 972–982

Citation in format AMSBIB

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\by V.~I.~Ivanov

\paper Direct and converse theorems of the theory of approximation in the metric of $L_p$ for $0<p<1$

\jour Mat. Zametki

\yr 1975

\vol 18

\issue 5

\pages 641--658

\mathnet{http://mi.mathnet.ru/mzm7677}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=412710}

\zmath{https://zbmath.org/?q=an:0337.42001}

\transl

\jour Math. Notes

\yr 1975

\vol 18

\issue 5

\pages 972--982

\crossref{https://doi.org/10.1007/BF01153563}

Linking options:

https://www.mathnet.ru/eng/mzm7677

https://www.mathnet.ru/eng/mzm/v18/i5/p641

This publication is cited in the following 17 articles:

S. Artamonov, K. Runovski, H.-J. Schmeisser, “Methods of trigonometric approximation and generalized smoothness. II”, Eurasian Math. J., 13:4 (2022), 18–43
M. Sh. Shabozov, E. U. Kadamshoev, “Sharp Inequalities between the Best Root-Mean-Square Approximations of Analytic Functions in the Disk and Some Smoothness Characteristics in the Bergman Space”, Math. Notes, 110:2 (2021), 248–260
K. V. Runovskii, “Generalized Smoothness and Approximation of Periodic Functions in the Spaces $L_p$ , $1<p<+\infty$ ”, Math. Notes, 106:3 (2019), 412–422
Yurii Kolomoitsev, Tetiana Lomako, Applied and Numerical Harmonic Analysis, Topics in Classical and Modern Analysis, 2019, 183
Yurii Kolomoitsev, “Best approximations and moduli of smoothness of functions and their derivatives in Lp, 0<p<1”, Journal of Approximation Theory, 232 (2018), 12
Yurii Kolomoitsev, “On moduli of smoothness and averaged differences of fractional order”, FCAA, 20:4 (2017), 988
Yurii Kolomoitsev, Jürgen Prestin, “Sharp estimates of approximation of periodic functions in Hölder spaces”, Journal of Approximation Theory, 200 (2015), 68
Yu. S. Kolomoitsev, “Approximation properties of generalized Bochner-Riesz means in the Hardy spaces $H_p$ , $0<p\le 1$ ”, Sb. Math., 203:8 (2012), 1151–1168
I. N. Katkovskaya, “Riesz' Compactness Criterion for the Space of Measurable Functions”, Math. Notes, 89:1 (2011), 145–149
K. Runovski, H.-J. Schmeisser, “Methods of trigonometric approximation and generalized smoothness. I”, Eurasian Math. J., 2:3 (2011), 98–124
V. I. Ivanov, “Direct and inverse theorems in approximation theory for periodic functions in S. B. Stechkins papers and the development of these theorems”, Proc. Steklov Inst. Math. (Suppl.), 273, suppl. 1 (2011), S1–S13
Yu. S. Kolomoitsev, “On approximation of functions by trigonometric polynomials with incomplete spectrum in $L_p$ , $0<p<1$ ”, J. Math. Sci. (N. Y.), 165:4 (2010), 463–472
È. A. Storozhenko, “Nikol'skii-Stechkin inequality for trigonometric polynomials in $L_0$ ”, Math. Notes, 80:3 (2006), 403–409
K. V. Runovskii, “Generalization of a theorem of Marcinkiewicz–Zygmund”, Math. Notes, 57:2 (1995), 180–183
V. G. Krotov, “On differentiability of functions in $L^p$ , $0<p<1$ ”, Math. USSR-Sb., 45:1 (1983), 101–119
È. A. Storozhenko, “Theorems of Jackson type in $H^p$ , $0<p<1$ ”, Math. USSR-Izv., 17:1 (1981), 203–218
È. A. Storozhenko, “Approximation of functions of class $H^p$ , $0<p\leqslant1$ ”, Math. USSR-Sb., 34:4 (1978), 527–545

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

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