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Approximation by Fourier sums of classes of functions with several bounded derivatives

  • é. M. Galeev
Article

Abstract

An ordered estimate is obtained for the approximation by Fourier sums, in the metric ofd=(d 1 , ...,d n ), 1<dj<∞,j=1, ...,n of classes of periodic functions of several variables with zero means with respect to all their arguments, having m mixed derivatives of order a1..., am., aiε rn. which are bounded in the metrics ofp i =p 1 i , ..., p n i , i<P j i <∞,i=i, ...,n, j=1, ...,n by the constants Β1, η., Βm, respectively.

Keywords

Fourier Periodic Function Mixed Derivative 
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Literature cited

  1. 1.
    O. V. Besov, V. P. Il'in, and S. M. Nikol'skii, Integral Representations of Functions and Imbedding Theorems [in Russian], Nauka, Moscow (1975).Google Scholar
  2. 2.
    O. V. Besov, “Multiplicative estimates for integral norms of differentiable functions of several variables,” Tr. Mat. Inst. Akad. Nauk SSSR,131, 3–15 (1974).Google Scholar
  3. 3.
    A. Zygmund, Trigonometric Series, Cambridge Univ. Press (1968).Google Scholar
  4. 4.
    V. M. Tikhomirov, “Diameters of sets in functional spaces and theory of best approximations,” Usp. Mat. Nauk,15, No. 3, 81–120 (1960).Google Scholar
  5. 5.
    R. T. Rockafellar, Convex Analysis, Princeton Univ. Press (1970).Google Scholar
  6. 6.
    V. M. Tikhomirov, Topics in Approximation Theory [in Russian], Moscow State Univ., Moscow (1976).Google Scholar
  7. 7.
    S. M. Nikol'skii, Approximation of Functions of Several Variables and Imbedding Theorems [in Russian], Nauka, Moscow (1969).Google Scholar
  8. 8.
    N. S. Nikol'skaya, “Approximation of differentiable functions of several variables by Fourier sums in the metric of Lp,” Dokl. Akad. Nauk SSSR,208, No. 6, 1282–1285 (1973).Google Scholar
  9. 9.
    N. S. Nikol'skaya, “Approximation of differentiable functions of several variables by Fourier sums in the metric of Lp,” Sib. Mat. Zh.,15, No. 2, 395–412 (1974).Google Scholar
  10. 10.
    G. H. Hardy, D. Littlewood, and G. Polya, Inequalities, Cambridge Univ. Press (1952).Google Scholar
  11. 11.
    B. S. Mityagin, “Approximation of functions in spaces C and Lp on a torus,” Mat. Sb.,58, No. 4, 397–414 (1962)Google Scholar

Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • é. M. Galeev
    • 1
  1. 1.Lomonosov Moscow State UniversityUSSR

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