RUS  ENG
Full version
JOURNALS // Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya

Izv. Akad. Nauk SSSR Ser. Mat., 1981, Volume 45, Issue 1, Pages 3–22 (Mi im1545)

On integral inequalities for trigonometric polynomials and their derivatives
V. V. Arestov

This publication is cited in the following articles:
  1. F. A. Bhat, “Refinement of Erdös-Lax inequality for $\mathrm{N}$-operator”, Probl. anal. Issues Anal., 14(32):1 (2025), 42–60  mathnet  crossref
  2. F. A. Bhat, H. A. Dar, H. A. Laway, “Integral mean extension of Turán type inequalities involving generalized polar derivative of a polynomial”, Indian J Pure Appl Math, 2025  crossref
  3. N. A. Rather, W. Naseer, S. Gulzar, “On $N$-Operators and Arestov's Inequalities within Schur–Szegő Compositions”, J. Contemp. Mathemat. Anal., 60:4 (2025), 320  crossref
  4. A. O. Leont'eva, “Bernstein Inequality for the Riesz Derivative of Order $0<\alpha<1$ of Entire Functions of Exponential Type in the Uniform Norm”, Math. Notes, 115:2 (2024), 205–214  mathnet  crossref  crossref  mathscinet  isi
  5. V. P. Zastavnyi, “On extremal functions in inequalities for entire functions”, Math. Notes, 116:1 (2024), 58–65  mathnet  crossref  crossref  isi
  6. N. A. Rather, N. Wani, A. Bhat, “Integral mean estimate for polynomials with restricted zeros”, Probl. anal. Issues Anal., 13(31):3 (2024), 101–117  mathnet  crossref
  7. Ahmad Motamednezhad, Fatemeh Mohammadi, “On the polar derivative of lacunary type polynomials”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 73:4 (2024), 1197  crossref
  8. M. Shafi, N. A. Rather, S. Gulzar, “A note on Visser's inequality”, Russian Math. (Iz. VUZ), 68:11 (2024), 44–52  mathnet  crossref  crossref
  9. A. O. Leont'eva, “Bernstein-Szegő inequality for the Riesz derivative of trigonometric polynomials in $L_p$-spaces, $0\leqslant p\leqslant\infty$, with classical value of the sharp constant”, Sb. Math., 214:3 (2023), 411–428  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
  10. V. P. Zastavnyi, “Ob ekstremalnykh trigonometricheskikh polinomakh”, Tr. IMM UrO RAN, 29, no. 4, 2023, 70–91  mathnet  crossref  elib
  11. A. O. Leont'eva, “On Constants in the Bernstein–Szegő Inequality for the Weyl Derivative of Order Less Than Unity of Trigonometric Polynomials and Entire Functions of Exponential Type in the Uniform Norm”, Proc. Steklov Inst. Math., 323: suppl. 1 (2023), S146–S154  mathnet  crossref  crossref  isi  elib
  12. A. O. Leont'eva, “Bernstein inequality for Riesz derivative of fractional order less than 1 of entire function of exponential type”, Dokl. Math., 108:3 (2023), 524–527  mathnet  crossref  crossref  elib
  13. Mudassir A. Bhat, Ravinder Kumar, Suhail Gulzar, “On Arestov's inequalities concerning the Shur–Szegő composition of polynomials”, Period Math Hung, 2023  crossref
  14. S. Gulzar, N. A. Rather, M. Sh. Wani, “On Visser's inequality concerning coefficient estimates for a polynomial”, Russian Math. (Iz. VUZ), 66:3 (2022), 9–15  mathnet  crossref  crossref
  15. A. O. Leonteva, “Neravenstvo Bernshteina - Sege dlya trigonometricheskikh polinomov v prostranstve $L_0$ s konstantoi bolshei, chem klassicheskaya”, Tr. IMM UrO RAN, 28, no. 4, 2022, 128–136  mathnet  crossref  elib
  16. Vitalii V. Arestov, Marina V. Deikalova, “On one inequality of different metrics for trigonometric polynomials”, Ural Math. J., 8:2 (2022), 27–45  mathnet  crossref  mathscinet
  17. N. A. Rather, A. Bhat, M. Shafi, “Integral inequalities for the growth and higher derivative of polynomials”, Proceedings of NAS RA. Mathematics, 2022, 64  crossref
  18. N. A. Rather, A. Bhat, M. Shafi, “Integral Inequalities for the Growth and Higher Derivative of Polynomials”, J. Contemp. Mathemat. Anal., 57:4 (2022), 242  crossref
  19. Nisar Ahmad Rather, Suhail Gulzar, Aijaz Bhat, “On Zygmund-type inequalities concerning polar derivative of polynomials”, Ural Math. J., 7:1 (2021), 87–95  mathnet  crossref  mathscinet  zmath
  20. D. V. Gorbachev, “Tochnye neravenstva Bernshteina — Nikolskogo dlya polinomov i tselykh funktsii eksponentsialnogo tipa”, Chebyshevskii sb., 22:5 (2021), 58–110  mathnet  crossref
  21. Xingjun Zhao, “Some inequalities for $s\mathrm{th}$ derivative of polynomials”, J Anal, 2021  crossref
  22. Dimitar K. Dimitrov, Geno P. Nikolov, “A discrete weighted Markov–Bernstein inequality for sequences and polynomials”, Journal of Mathematical Analysis and Applications, 493:1 (2021), 124522  crossref
  23. R. N. Akhmad, A. Liiakat, G. Sukhail, “$L_p$-neravenstva dlya polyarnoi proizvodnoi polinoma lakunarnogo tipa”, Vestnik Sankt-Peterburgskogo universiteta. Matematika. Mekhanika. Astronomiya, 8:3 (2021), 502–510  mathnet  crossref
  24. S. L. Wali, “An integral estimate for an operator preserving inequalities between polynomials”, Probl. anal. Issues Anal., 9(27):3 (2020), 137–147  mathnet  crossref
  25. A. V. Kroó, “On a refinement of Marcinkiewicz-Zygmund type inequalities”, Tr. IMM UrO RAN, 26, no. 4, 2020, 196–209  mathnet  crossref
  26. Alexandros Eskenazis, Paata Ivanisvili, “Dimension independent Bernstein–Markov inequalities in Gauss space”, Journal of Approximation Theory, 253 (2020), 105377  crossref
  27. K. V. Runovskii, “Generalized Smoothness and Approximation of Periodic Functions in the Spaces $L_p$, $1<p<+\infty$”, Math. Notes, 106:3 (2019), 412–422  mathnet  crossref  crossref  mathscinet  isi  elib
  28. A. O. Leont'eva, “Bernstein's Inequality for the Weyl Derivatives of Trigonometric Polynomials in the Space $L_0$”, Math. Notes, 104:2 (2018), 263–270  mathnet  crossref  crossref  mathscinet  isi  elib
  29. A. O. Leont'eva, “Bernstein–Szegő Inequality for the Weyl Derivative of Trigonometric Polynomials in $L_0$”, Proc. Steklov Inst. Math., 308: suppl. 1 (2020), S127–S134  mathnet  crossref  crossref  isi  elib
  30. P. Yu. Glazyrina, Sz. Gy. Révész, “Turán–Erőd type converse Markov inequalities on general convex domains of the plane in the boundary $L^q$ norm”, Proc. Steklov Inst. Math., 303 (2018), 78–104  mathnet  crossref  crossref  mathscinet  isi  elib
  31. Viktor P. Zastavnyi, “Positive definite functions and sharp inequalities for periodic functions”, Ural Math. J., 3:2 (2017), 82–99  mathnet  crossref  mathscinet
  32. S. Gulzar, N. A. Rather, “L p inequalities for the Schur–Szegő composition of polynomials”, Acta Math. Hungar., 151:1 (2017), 124  crossref
  33. Igor E. Pritsker, Springer Optimization and Its Applications, 117, Progress in Approximation Theory and Applicable Complex Analysis, 2017, 83  crossref
  34. Arestov V., Deikalova M., “Nikol'skii inequality between the uniform norm and L q -norm with Jacobi weight of algebraic polynomials on an interval”, Anal. Math., 42:2 (2016), 91–120  crossref  mathscinet  isi  elib  scopus
  35. Feng Dai, Sergey Tikhonov, “Weighted fractional Bernstein's inequalities and their applications”, JAMA, 129:1 (2016), 33  crossref
  36. Vitalii Arestov, Marina Deikalova, “Nikol’skii Inequality Between the Uniform Norm and
    $$\varvec{L_q}$$
    L q -Norm with Ultraspherical Weight of Algebraic Polynomials on an Interval”, Comput. Methods Funct. Theory, 2015  crossref
  37. È. A. Storozhenko, L. G. Kovalenko, “Inequality for Fractional Integrals of Complex Polynomials in $L_0$”, Math. Notes, 96:4 (2014), 609–612  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  38. I.E.. Simonov, P.Y.u. Glazyrina, “Sharp Markov–Nikol’skii inequality with respect to the uniform norm and the integral norm with Chebyshev weight”, Journal of Approximation Theory, 2014  crossref
  39. V. V. Arestov, P. Yu. Glazyrina, “Bernstein–Szegö inequality for fractional derivatives of trigonometric polynomials”, Proc. Steklov Inst. Math., 288: suppl. 1 (2015), S13–S28  mathnet  crossref  mathscinet  isi  elib
  40. A. O. Leonteva, “Neravenstvo Bernshteina v $L_0$ dlya proizvodnoi nulevogo poryadka trigonometricheskikh polinomov”, Tr. IMM UrO RAN, 19, no. 2, 2013, 216–223  mathnet  mathscinet  elib
  41. V. V. Arestov, M. V. Deikalova, “Nikol'skii inequality for algebraic polynomials on a multidimensional Euclidean sphere”, Proc. Steklov Inst. Math., 284: suppl. 1 (2014), S9–S23  mathnet  crossref  mathscinet  isi  elib
  42. Abdullah Mir, Sajad Amin Baba, “Some integral inequalities for the polar derivative of a polynomial”, Anal. Theory Appl, 27:4 (2012), 340  crossref
  43. V. V. Arestov, P. Yu. Glazyrina, “Integral inequalities for algebraic and trigonometric polynomials”, Dokl. Math, 85:1 (2012), 104  crossref
  44. Arestov V.V., Glazyrina P.Yu., “Integralnye neravenstva dlya algebraicheskikh i trigonometricheskikh polinomov”, Doklady Akademii nauk, 442:6 (2012), 727–727  elib
  45. Abdul Aziz, N.A.. Rather, “L<sup>p</sup> Inequalities for Polynomials”, AM, 02:03 (2011), 321  crossref
  46. V. V. Arestov, “Sharp inequalities for trigonometric polynomials with respect to integral functionals”, Proc. Steklov Inst. Math., 273: suppl. 1 (2011), S21–S36  mathnet  crossref  isi  elib
  47. A. V. Parfenenkov, “Tochnoe neravenstvo mezhdu ravnomernymi normami algebraicheskogo mnogochlena i ego veschestvennoi chasti na kontsentricheskikh okruzhnostyakh kompleksnoi ploskosti”, Tr. IMM UrO RAN, 16, no. 4, 2010, 254–263  mathnet  elib
  48. M. A. Qazi, Q. I. Rahman, “An L 2 inequality for rational functions”, Complex Variables & Elliptic Equations, 55:7 (2010), 657  crossref
  49. St. Petersburg Math. J., 21:3 (2010), 365–405  mathnet  crossref  mathscinet  zmath  isi
  50. Rajesh Pereira, “Product inequalities for norms of linear factors”, Journal of Mathematical Analysis and Applications, 356:1 (2009), 208  crossref
  51. M.A. Qazi, Q.I. Rahman, “A question concerning a polynomial inequality and an answer”, Nonlinear Analysis: Theory, Methods & Applications, 71:12 (2009), e2710  crossref
  52. A. Aziz, W. M. Shah, “Some integral mean estimates for polynomials”, Analys in Theo Applic, 23:2 (2007), 101  crossref  mathscinet
  53. A. B. Aleksandrov, “Spectral subspaces of $L^p$ for $p<1$”, St. Petersburg Math. J., 19:3 (2008), 327–374  mathnet  crossref  mathscinet  zmath  isi
  54. R. R. Akopian, “Optimal recovery of functions analytical in a half-plane”, Proc. Steklov Inst. Math., 259: suppl. 2 (2007), S1–S11  mathnet  crossref  elib
  55. M.A. Qazi, “An inequality for polynomials”, Journal of Mathematical Analysis and Applications, 336:2 (2007), 1456  crossref
  56. È. A. Storozhenko, “Nikol'skii-Stechkin inequality for trigonometric polynomials in $L_0$”, Math. Notes, 80:3 (2006), 403–409  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  57. P. Yu. Glazyrina, “The Markov Brothers Inequality in $L_0$-Space on an Interval”, Math. Notes, 78:1 (2005), 53–58  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  58. P. Yu. Glazyrina, “Markov–Nikol'skii inequality for the spaces $L_q$, $L_0$ on a segment”, Proc. Steklov Inst. Math., 2005, suppl. 2, S104–S116  mathnet  mathscinet  zmath  elib
  59. A. I. Kozko, “Fractional derivatives and inequalities for trigonometric polynomials in spaces with asymmetric norms”, Izv. Math., 62:6 (1998), 1189–1206  mathnet  crossref  crossref  mathscinet  zmath  isi
  60. Robert Gardner, Amy Weems, “A Bernstein TypeLpInequality for a Certain Class of Polynomials”, Journal of Mathematical Analysis and Applications, 219:2 (1998), 472  crossref
  61. R. M. Trigub, “Multipliers in the Hardy spaces $H_p(D^m)$ with $p\in (0,1]$ and approximation properties of summability methods for power series”, Sb. Math., 188:4 (1997), 621–638  mathnet  crossref  crossref  mathscinet  zmath  isi
  62. È. A. Storozhenko, “A problem of Mahler on the zeros of a polynomial and its derivative”, Sb. Math., 187:5 (1996), 735–744  mathnet  crossref  crossref  mathscinet  zmath  isi
  63. Z. Ditzian, V. H. Hristov, K. G. Ivanov, “Moduli of smoothness andK-functionals inL p, 0<p<1”, Constr. Approx, 11:1 (1995), 67  crossref
  64. V. V. Arestov, “The Szegő inequality for derivatives of a conjugate trigonometric polynomial in $L_0$”, Math. Notes, 56:6 (1994), 1216–1227  mathnet  crossref  mathscinet  zmath  isi
  65. Albert Baernstein, “An extremal property of meromorphic functions withn–fold symmetry”, Complex Variables, Theory and Application: An International Journal, 21:3-4 (1993), 137  crossref
  66. Z Ditzian, “Multivariate Bernstein and Markov inequalities”, Journal of Approximation Theory, 70:3 (1992), 273  crossref
  67. Q.I Rahman, G Schmeisser, “Lp inequalities for polynomials”, Journal of Approximation Theory, 53:1 (1988), 26  crossref


© Steklov Math. Inst. of RAS, 2026