On the growth of mth derivatives of algebraic polynomials in the weighted Lebesgue space

References

• Walsh JL. Interpolation and approximation by rational functions in the complex domain. Providence Rhode Island: AMS; 1960.
   Google Scholar
• Hille E, Szegö G, Tamarkin JD. On some generalization of a theorem of A.Markoff. Duke Math J. 1937;3:729–739.
   Google Scholar
• Abdullayev FG, Özkartepe P. On the growth of algebraic polynomials in the whole complex plane. J Korean Math Soc. 201552(4):699–725.
   Web of Science ®Google Scholar
• Pommerenke Ch. Univalent functions. Göttingen: Vandenhoeck & Ruprecht; 1975.
   Google Scholar
• Belinskii PP. General properties of quasiconformal mappings. Novosibirsk: Nauka, Sib. otd.; 1974. Russian.
   Google Scholar
• Lehto O, Virtanen KI. Quasiconformal mapping in the plane. Berlin: Springer; 1973.
   Google Scholar
• Abdullayev FG. On the some properties on orthogonal polynomials over the regions of complex plane 1. Ukr Math J. 2000;52(12):1807–1817.
   Google Scholar
• Abdullayev FG, Özkartepe P. An analogue of the Bernstein–Walsh lemma in Jordan regions of the complex plane. J Inequal Appl. 20131(2013):1–7.
   Google Scholar
• Stylianopoulos N. Strong asymptotics for Bergman polynomials over domains with corners and applications. Constr Approx. 2012;38(1):59–100.
   Web of Science ®Google Scholar
• Abdullayev FG, Özkartepe P. On the behavior of the algebraic polynomial in unbounded regions with piecewise dini-smooth boundary. Ukr Math J. 2014;66(5):645–665.
   Web of Science ®Google Scholar
• Abdullayev FG, Özkartepe P, Gün CD. Uniform and pointwise polynomial inequalities in regions without cusps in the weighted Lebesgue space. Bull TICMI. 2014;18(1):146–167.
   Google Scholar
• Abdullayev FG, Gün CD, Ozkartepe NP. Inequalıtıes for algebraıc polynomıals ın regıons wıth exterıor cusps. J Nonlinear Funct Anal. 2015;3:1–32.
   Google Scholar
• Abdullayev FG, Özkartepe P. Uniform and pointwise polynomial inequalities in regions with cusps in the weighted Lebesgue space. Jaen J Approx. 2015;7(2):231–261.
   Google Scholar
• Abdullayev FG, Özkartepe NP. Polynomial inequalities in Lavrentiev regions with interior and exterior zero angles in the weighted Lebesgue space. Publ l'Inst Math (Beograd). 2016;100(114):209–227.
   Google Scholar
• Abdullayev FG, Özkartepe NP. Interference of the weight and boundary contour for algebraic polynomials in the weighted Lebesgue spaces. I. Ukr Math J. 201768(10):1574–1590. (Translated from Ukr Mat Zh. 2016;68(10):1365–1379.)
   Web of Science ®Google Scholar
• Abdullayev FG. Polynomial inequalities in regions with corners in the weighted Lebesgue spaces. Filomat. 2017;31(18):5647–5670.
   Web of Science ®Google Scholar
• Abdullayev FG, Imashkyzy M, Abdullayeva G. Bernstein–Walsh type inequalities in unbounded regions with piecewise asymptotically conformal curve in the weighted Lebesgue space. J Math Sci. 2018;234(1):35–48. DOI:10.1007/s10958-018-3979-6. (Translated from Ukr Mat Visnik. 2017;14(4):515–531.)
   Google Scholar
• Abdullayev FG, Tunc T, Abdullayev GA. Polynomial inequalities in quasidisks on weighted Bergman space. Ukr Math J. 2017;69(5):675–695.
   Web of Science ®Google Scholar
• Abdullayev FG, Özkartepe NP. The uniform and pointwise estimates for polynomials on the weighted Lebesgue spaces in the general regions of complex plane. Hacet J Math Stat. 2019;48(1):87–101.
   Web of Science ®Google Scholar
• Abdullayev FG, Özkartepe P, Tunç T. Uniform and pointwise estimates for algebraic polynomials in regions with interior and exterior zero angles. Filomat. 2019;33(2):403–413.
   Web of Science ®Google Scholar
• Abdullayev FG, Gün CD. Bernstein–Walsh-type inequalities for derivatives of algebraic polynomials. Bull Korean Math Soc. 2022;59(1):45–72. DOI:10.4134/BKMS.b210023
   Web of Science ®Google Scholar
• Abdullayev FG. Bernstein–Walsh-type inequalities for derivatives of algebraic polynomials in quasidiscs. OPEN Math. 2022;19(1):1847–1876.
   Web of Science ®Google Scholar
• Dzjadyk VK. Introduction to the theory of uniform approximation of functiıon by polynomials. Moskow: Nauka; 1977.
   Google Scholar
• Mamedhanov DI. Inequalities of S.M.Nikol'skii type for polynomials in the complex variable on curves. Sov Math Dokl. 1974;15:34–37.
   Google Scholar
• Bernstein SN. Sur la limitation des derivees des polnomes. C R Acad Sci Paris. 1930;190:338–341.
   Google Scholar
• Bernstein SN. On the best approximation of continuos functions by polynomials of given degree. Izd. Akad. Nauk SSSR I. 1952; II; 1954 (O nailuchshem problizhenii nepreryvnykh funktsii posredstrvom mnogochlenov dannoi stepeni). Sobraniye Sochinenii. 1912;I(4):11–10.
   Google Scholar
• Szegö G, Zygmund A. On certain mean values of polynomials. J Anal Math. 1953;3(1):225–244.
   Google Scholar
• Abdullayev FG. On some properties of the orthogonal polynomials over the region of the complex plane (Part III). Ukr Math J. 2001;53(12):1934–1948.
   Google Scholar
• Abdullayev FG. The properties of the orthogonal polynomials with weight having singularity on the boundary contour. J Comput Anal Appl. 2004;6(1):43–59.
   Google Scholar
• Abdullayev FG. On the interference of the weight boundary contour for orthogonal polynomials over the region. J Comput Anal Appl. 2004;6(1):31–42.
   Google Scholar
• Abdullayev FG, Gün CD. Bernstein–Nikolskii-type inequalities for algebraic polynomials in Bergman space in regions of complex plane. Ukr Math J. 202173(4):513–531. (Translated from Ukr Mat Zh. 2021 Apr;73(4):439–454.)
   Web of Science ®Google Scholar
• Andrievskii VV. Weighted polynomial inequalities in the complex plan. J Approx Theory. 2012;164(9):1165–1183.
   Web of Science ®Google Scholar
• Balcı S, Imashkyzy M, Abdullayev FG. Polynomial inequalities in regions with interior zero angles in the Bergman space. Ukr Math J. 2018;70(3):362–384.
   Web of Science ®Google Scholar
• Benko D, Dragnev P, Totik V. Convexity of harmonic densities. Rev Mat Iberoamericana. 2012;28(4):1–14.
   Web of Science ®Google Scholar
• Ditzian Z, Tikhonov S. Ul'yanov and Nikol'skii-type inequalities. J Approx Theory. 2005;133(1):100–133. DOI:10.1016/j.jat.2004.12.008 .
   Web of Science ®Google Scholar
• Ditzian Z, Prymak A. Nikol'skii inequalities for Lorentz spaces. Rocky Mountain J Math. 2010;40(1):209–223.
   Web of Science ®Google Scholar
• Milovanovic GV, Mitrinovic DS, Rassias ThM. Topics in polynomials: extremal problems, inequalities, zeros. Singapore: World Scientific; 1994.
   Google Scholar
• Nevai P, Totik V. Sharp Nikolskii inequalities with exponential weights. Anal Math. 1987;13(4):261–267.
   Google Scholar
• Nikol'skii SM. Approximation of function of several variable and imbeding theorems. New York: Springer; 1975.
   Google Scholar
• Pritsker I. Comparing norms of polynomials in one and several variables. J Math Anal Appl. 1997;216:685–695. DOI:10.1006/jmaa.1997.5699
   Web of Science ®Google Scholar
• Lesley FD. Hölder continuity of conformal mappings at the boundary via the strip method. Indiana Univ Math J. 1982;31:341–354.
   Web of Science ®Google Scholar
• Becker J, Pommerenke C. Uber die quasikonforme Fortsetzung schlichten Funktionen. Math Z. 1978;161:69–80.
   Web of Science ®Google Scholar
• Pommerenke Ch. Boundary behaviour of conformal maps. Berlin: Springer; 1992.
   Google Scholar
• Ahlfors L. Lectures on quasiconformal mappings. Princeton (NJ): Van Nostrand; 1966.
   Google Scholar
• Warschawski SE. On differentiability at the boundary in conformal mapping. Proc Am Math Soc. 1961;12:614–620.
   Google Scholar
• Warschawski SE. On Hölder continuity at the boundary in conformal maps. J Math Mech. 1968;18:423–427.
   Google Scholar
• Abdullayev FG, Andrievskii VV. On the orthogonal polynomials in the domains with K-quasiconformal boundary. Izv Akad Nauk Azerb SSR Ser FTM. 1983;1:3–7.
   Google Scholar
• Andrievskii VV, Belyi VI, Dzyadyk VK. Conformal invariants in constructive theory of functions of complex plane. Atlanta: World Federation; 1995.
   Google Scholar