A Bernstein-Nikol'skii inequality for weighted Lebesgue spaces

Автор: Bang Ha Huy, Huy Vu Nhat

Журнал: Владикавказский математический журнал @vmj-ru

Статья в выпуске: 3 т.22, 2020 года.

Бесплатный доступ

In this paper, we give some results concerning Bernstein-Nikol'skii inequality for weighted Lebesgue spaces. The advantage of our result is that m-ϱ appears on the right hand side of the inequality (ϱ>0), which has never appeared in related articles by other authors. The corresponding result for the n-dimensional case is also obtained.

Weighted lebesgue spaces, bernstein inequality, nikol'skii inequality

Короткий адрес: https://readera.org/143172453

IDR: 143172453   |   DOI: 10.46698/h8083-6917-3687-w

Список литературы A Bernstein-Nikol'skii inequality for weighted Lebesgue spaces

  • Bernstein, S. N. Sur l'Ordre de la Meilleure Approximation des Functions Continues par les Polyomes de Degre Donne, Extrait des Memoires de l'Academie royale de Belgque, ser. 2, vol. 4, Bruxelles, Hayez, 1912, 103 p.
  • DeVore, R. and Lorentz, G. G. Constructive Approximation, Springer-Verlag, Berlin, 1993.
  • Nikol'skii, S. M. Approximation of Functions of Several Variables and Imbedding Theorems, Grundl. Math. Wissensch, vol. 205, Berlin, Springer-Verlag, 1975. DOI: 10.1007/978-3-642-65711-5
  • Nikol'skii, S. M. Inequalities for Entire Functions of Finite Degree and their Application to the Theory of Differentiable Functions of Several Variables, Trudy Matematicheskogo Instituta imeni V.A. Steklova [Proceedings of the Steklov Institute of Mathematics], vol. 38, Moscow, Acad. Sci. USSR, 1951, pp. 244-278 (in Russian).
  • Frappier, C. and Rahman, Q. I. On an Inequality of S. Bernstein, Canadian Journal of Mathematics, 1982, vol. 34, pp. 932-944. DOI: 10.4153/CJM-1982-066-7
  • Ganzburg, M. I. Sharp constants in V. A. Markov-Bernstein Type Inequalities Of Different Metrics, Journal of Approximation Theory, 2017, vol. 215, pp. 92-105.
  • DOI: 10.1016/j.jat.2016.11.007
  • Ganzburg, M. I. Sharp Constants of Approximation Theory. I. Multivariate Bernstein-Nikolskii Type Inequalities, Journal of Fourier Analysis and Applications, 2020, vol. 26, article 11.
  • DOI: 10.1007/s00041-019-09720-x
  • Ganzburg, M. I. and Tikhonov, S. Yu. On Sharp Constants in Bernstein-Nikolskii Inequalities, Constructive Approximation, 2017, vol. 45, pp. 449-466.
  • DOI: 10.1007/s00365-016-9363-1
  • Platonov, S. S. Bessel Harmonic Analysis and the Approximation of Functions on a Half-Line, Izvestiya: Mathematics, 2007, vol. 71, no. 5, pp. 1001-1048.
  • Rahman, Q. I. and Schmeisser, G. Lp Inequalities for Entire Functions of Exponential Type, Transactions of the American Mathematical Society, 1990, vol. 320, pp. 91-103.
  • DOI: 10.1090/S0002-9947-1990-0974526-4
  • Rahman, Q. I. and Tariq, Q. M. On Bernstein's Inequality for Entire Functions of Exponential Type, Computational Methods and Function Theory, 2007, vol. 7, pp. 167-184.
  • DOI: 10.1007/BF03321639
  • Nessel, R. J. and Wilmes, G. Nikol'skii-Type Inequalities in Connection with Regular Spectral Measures, Acta Mathematica, 1979, vol. 33, pp. 169-182.
  • Nessel, R. J. and Wilmes, G. Nikol'skii-Type Inequalities for Trigonometric Polynomials and Entire Functions of Exponential Type, Journal of the Australian Mathematical Society, 1978, vol. 25, pp. 7-18.
  • DOI: 10.1017/S1446788700038878
  • Nikol'skii, S. M. Some Inequalities for Entire Functions of Finite Degree and their Application, Doklady Akademii Nauk SSSR, 1951, vol. 76, pp. 785-788 (in Russian).
  • Triebel, H. General Function Spaces, II: Inequalities of Plancherel-Polya Nikolskii-type, Lp-Space of Analytic Functions: 0
  • Triebel, H. Theory of Function Spaces, Basel, Boston, Stuttgart, Birkhauser, 1983.
  • Bang, H. H. and Huy, V. N. New Results Concerning the Bernstein-Nikol'skii Inequality, Advances in Mathematics Reseach, 2011, vol. 16, pp. 177-191.
  • Bang, H. H. A Property of Infinitely Differentiable Functions, Proceedings of the American Mathematical Society, 1990, vol. 108, pp. 73-76.
  • DOI: 10.1090/S0002-9939-1990-1024259-9
  • Kerman, R. A. Convolution Theorems with Weights, Transactions of the American Mathematical Society, 1983, vol. 280, no. 1, pp. 207-219.
  • DOI: 10.1090/S0002-9947-1983-0712256-0
  • Vladimirov, V. S. Methods of the Theory of Generalized Functions, Taylor & Francis, London, New York, 2002.
Еще
Статья научная