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Exact Classical Polynomial Inequalities In H p for 0 ≤ p ≤ ∞

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Recent Progress in Inequalities

Part of the book series: Mathematics and Its Applications ((MAIA,volume 430))

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Abstract

This paper is devoted to the exact Bernstein, Szegő and Zygmund inequalities for trigonometric polynomials (on the real line) and for algebraic polynomials on the unit disk in the complex plane, as well as to some more general inequalities.

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References

  1. V. V. Arestov On inequalities of S. N. Bernstein for algebraic and trigonometric polynomials, Soviet Math. Dokl. 20 (1979), 600–603.

    MATH  Google Scholar 

  2. V. V. Arestov, Integral inequalities for trigonometric polynomials and their derivatives, Izv. AN SSSR Ser. Mat. 45 (1981), 3–22 (Russian) [Engl. Trans.: Math. USSR-Izv. 18 (1982), 1-17].

    MathSciNet  Google Scholar 

  3. V. V. Arestov, Integral inequalities for algebraic polynomials on the unit circle, Mat. Zametki 48 (1990), 7–18. (Russian)

    MathSciNet  MATH  Google Scholar 

  4. V. V. Arestov, On one Szegö inequality for algebraic polynomials, Trudy Inst. Mat. Mekh. (Ekaterinburg) 2 (1992), 27–33.

    MathSciNet  MATH  Google Scholar 

  5. V. V. Arestov, The Szegö inequality for derivatives of a conjugate trigonometric polynomial in L o, Math. Notes 56 (1994), 1216–1227.

    Article  MathSciNet  MATH  Google Scholar 

  6. S. N. Bernstein Sur Vordre de la mailleure approximation des fonctions continues par des polynômes de degré donné, Mémoires de l’Académie Royale de Belgique (2) 4 (1912), 1–103.

    Google Scholar 

  7. V. V. Arestov, Leçons sur les propriétés extrémales et la meilleure approximation des fonctions analytiques d’une variable réele, Collection Borel, Paris, 1926.

    Google Scholar 

  8. N. G. de Bruijn and T. A. Springer, On the zeros of composition-polynomials, Nederl. Akad. Wetensch. Proc. 50 (1947), 895–903 [= Indag. Math. 9 (1947), 406-414].

    MathSciNet  MATH  Google Scholar 

  9. V. I. Ivanov, Some inequalities for trigonometric polynomials and their derivatives in different metrics, Mat. Zametki 18 (1975), 489–498. (Russian)

    MathSciNet  MATH  Google Scholar 

  10. M. Marden, The Geometry of the Zeros of a Polynomials in a Complex Variable, Math. Survey, No. 3, Amer. Math. Soc, New York, 1949.

    Google Scholar 

  11. G. Polyá and G. Szegö, Problems and Theorems in Analysis, Vols. I and II, Springer Verlag, Berlin, 1976.

    Google Scholar 

  12. M. Riesz Eine trigonometrische Interpolationsformel und einige Ungleichungen für Polynome, Jahresbericht der Deutschen Mathematiker-Vereinigung 23 (1914), 354–368.

    MATH  Google Scholar 

  13. E. A. Storozenko, V. G. Krotov and P. Osval’d, Direct and converse theorems of Jackson type in L P spaces, 0 < p < 1, Mat. Sb. (N.S.) 98(140) (1975), 395–415. (Russian)

    MathSciNet  Google Scholar 

  14. G. Szegö Über einen Satz des Herrn Serge Bernstein, Schrift. Königsberg. Gelehrten Gesellschaft. 5 (1928), 59–70.

    Google Scholar 

  15. A. Zygmund, Trigonometric Series, Vols. I and II, Cambridge Univ. Press, Cambridge, 1965.

    MATH  Google Scholar 

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Arestov, V.V. (1998). Exact Classical Polynomial Inequalities In H p for 0 ≤ p ≤ ∞. In: Milovanović, G.V. (eds) Recent Progress in Inequalities. Mathematics and Its Applications, vol 430. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9086-0_4

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  • DOI: https://doi.org/10.1007/978-94-015-9086-0_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4945-2

  • Online ISBN: 978-94-015-9086-0

  • eBook Packages: Springer Book Archive

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