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Mat. Sb., 1993, Volume 184, Number 2, Pages 33–42 (Mi msb962)  

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

On families of linear polynomial operators in $L_p$-spaces, $0<p<1$

K. V. Runovskii

T. H. Shevchenko Chernihiv State Pedagogical Institute

Abstract: Questions of approximation of periodic functions in $L_p$-spaces for $0<p<1$ by certain families of linear polynomial operators are studied. Some applications are given for the method developed.

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English version:
Russian Academy of Sciences. Sbornik. Mathematics, 1994, 78:1, 165–173

Bibliographic databases:

UDC: 517.51
MSC: Primary 41A35; Secondary 46E30
Received: 02.10.1991

Citation: K. V. Runovskii, “On families of linear polynomial operators in $L_p$-spaces, $0<p<1$”, Mat. Sb., 184:2 (1993), 33–42; Russian Acad. Sci. Sb. Math., 78:1 (1994), 165–173

Citation in format AMSBIB
\by K.~V.~Runovskii
\paper On families of linear polynomial operators in $L_p$-spaces, $0<p<1$
\jour Mat. Sb.
\yr 1993
\vol 184
\issue 2
\pages 33--42
\jour Russian Acad. Sci. Sb. Math.
\yr 1994
\vol 78
\issue 1
\pages 165--173

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    This publication is cited in the following articles:
    1. K. V. Runovskii, “On approximation by families of linear polynomial operators in $l_P$-spaces, $0<p<1$”, Russian Acad. Sci. Sb. Math., 82:2 (1995), 441–459  mathnet  crossref  mathscinet  zmath  isi
    2. K. V. Runovskii, “Generalization of a theorem of Marcinkiewicz–Zygmund”, Math. Notes, 57:2 (1995), 180–183  mathnet  crossref  mathscinet  zmath  isi  elib
    3. K. V. Runovskii, H. J. Schmeisser, “On Marcinkiewicz-Zygmund Type Inequalities for Irregular Knots inLp-Spaces, 0 <p ≦ +∞”, Math Nachr, 189:1 (1998), 209  crossref  mathscinet  zmath  isi
    4. Burinska Z. Runovski K. Schmeisser H., “On the Method of Approximation by Families of Linear Polynomial Operators”, Z. Anal. ihre. Anwend., 19:3 (2000), 677–693  mathscinet  zmath  isi
    5. Ditzian Z. Runovskii K., “Realization and Smoothness Related to the Laplacian”, Acta Math. Hung., 93:3 (2001), 189–223  crossref  mathscinet  zmath  isi
    6. Runovski K. Rystsov I. Schmeisser H.-J., “Computational Aspects of a Method of Stochastic Approximation”, Z. Anal. ihre. Anwend., 25:3 (2006), 367–383  crossref  mathscinet  zmath  isi
    7. Konstantin Runovski, Hans-Jürgen Schmeisser, “On Approximation Methods Generated by Bochner-Riesz Kernels”, J Fourier Anal Appl, 14:1 (2008), 16  crossref  mathscinet  zmath  isi
    8. 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  mathnet  crossref  elib
    9. K. Runovski, H.-J. Schmeisser, “On convergence of families of linear polynomial operators generated by matrices of multipliers”, Eurasian Math. J., 1:3 (2010), 112–133  mathnet  mathscinet  zmath
    10. 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  mathnet  crossref  elib
    11. K.  Runovski, H.-J. Schmeisser, “On families of linear polynomial operators generated by Riesz kernels”, Eurasian Math. J., 1:4 (2010), 124–139  mathnet  mathscinet  zmath
    12. F. Dai, Z. Ditzian, “Jackson theorem in , for functions on the sphere”, Journal of Approximation Theory, 162:2 (2010), 382  crossref
    13. Vladimir Rukasov, Konstantin Runovski, Hans-Jürgen Schmeisser, “Approximation by families of linear trigonometric polynomial operators and smoothness properties of functions”, Math. Nachr, 2011, n/a  crossref
    14. K. Runovski, H.-J. Schmeisser, “Methods of trigonometric approximation and generalized smoothness. I”, Eurasian Math. J., 2:3 (2011), 98–124  mathnet  mathscinet  zmath
    15. Akgun R., “Approximation by Polynomials in Rearrangement Invariant Quasi Banach Function Spaces”, Banach J. Math. Anal., 6:2 (2012), 113–131  mathscinet  zmath  isi
    16. K. V. Runovskii, N. V. Omel'chenko, “Mixed Generalized Modulus of Smoothness and Approximation by the “Angle” of Trigonometric Polynomials”, Math. Notes, 100:3 (2016), 448–457  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    17. K. V. Runovski, “Trigonometric polynomial approximation, $K$-functionals and generalized moduli of smoothness”, Sb. Math., 208:2 (2017), 237–254  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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