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Certain exact bounds for seminorms given on spaces of periodic functions

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Abstract

Certain new bounds are established for the values of seminorms given on the spaces C and Lp (1⩽p<∞) of periodic functions by means of the norm of the function itself and its finite differences, as well as of the moduli of continuity. These bounds are applied to concrete seminorms; in particular, to the best approximation, which yields a refinement of the direct theorems in approximation theory. The results obtained for spaces C and L1 are exact.

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Literature cited

  1. A. A. Ligun, “Exact inequalities for the upper bounds on a seminorm on classes of periodic functions,” Mat. Zametki,13, No. 5, 647–654 (1973).

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Authors and Affiliations

  1. Leningrad State University, USSR

    V. V. Zhuk

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  1. V. V. Zhuk
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Translated from Matematicheskie Zametki, Vol. 21, No. 6, pp. 789–798, June, 1977.

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Zhuk, V.V. Certain exact bounds for seminorms given on spaces of periodic functions. Mathematical Notes of the Academy of Sciences of the USSR 21, 445–450 (1977). https://doi.org/10.1007/BF01410172

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  • DOI: https://doi.org/10.1007/BF01410172

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