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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 48 Issue: 1

The uniform and pointwise estimates for polynomials on the weighted Lebesgue spaces in the general regions of complex plane

P. Özkartepe
F.g. Abdullayev
Pages
—
Publication Date
2019-02-01
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⚡ TL;DR(Too Long; Didn't Read)

The estimation of the modulus of algebraic polynomials on the boundary contour with weight function, having some singularities, with respect to the their quasinorm, on the weighted Lebesgue space was studied in this current work.

📌 3 Key Takeaways

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Objective & Hypothesis:The estimation of the modulus of algebraic polynomials on the boundary contour with weight function, having some singularities, with respect to the their quasinorm, on the weighted Lebesgue space was studied in this current work.
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Key Findings & Data:The estimation of the modulus of algebraic polynomials on the boundary contour with weight function, having some singularities, with respect to the their quasinorm, on the weighted Lebesgue space was studied in this current work.
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Conclusion & Impact:The estimation of the modulus of algebraic polynomials on the boundary contour with weight function, having some singularities, with respect to the their quasinorm, on the weighted Lebesgue space was studied in this current work.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:algebraic polynomials · conformal mapping · quasicircle

Abstract

The estimation of the modulus of algebraic polynomials on the boundary contour with weight function, having some singularities, with respect to the their quasinorm, on the weighted Lebesgue space was studied in this current work.

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Cite This Article

Özkartepe, P., Abdullayev, F. (2019). The uniform and pointwise estimates for polynomials on the weighted Lebesgue spaces in the general regions of complex plane. Hacettepe Journal of Mathematics and Statistics, Volume: 48 Issue: 1. https://doi.org/10.15672/HJMS.2018.639

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References (31)

  1. F.G. Abdullayev, On the some properties on orthogonal polynomials over the regions of complex plane 1. Ukr. Math. J. 52 (12), 1807-1817, 2000.
  2. F.G. Abdullayev, On the interference of the weight boundary contour orthogonal polynomials over the region, J. of Comp. Anal. and Appl. 6 (1), 31-42, 2004.
  3. F.G. Abdullayev and V.V. Andrievskii, On the orthogonal polynomials in the domains with $K$-quasiconformal boundary, Izv. Akad. Nauk Azerb. SSR., Ser. FTM, 1, 3-7, 1983.
  4. F.G. Abdullayev and C.D. Gün, On the behavior of the algebraic polynomials in regions with piecewise smooth boundary without cusps, Ann. Polon. Math. 111, 39-58, 2014.
  5. F.G. Abdullayev and N.P. Özkartepe, On the Behavior of the Algebraic Polynomial in Unbounded Regions with Piecewise Dini -Smooth Boundary, Ukr. Math. J., 66 (5), 579-597, 2014.
  6. F.G. Abdullayev and N.P. Özkartepe, On the growth of algebraic polynomials in the whole complex plane, J. Korean Math. Soc. 52 (4) 699-725, 2015.
  7. F.G. Abdullayev and N.P. Özkartepe, Uniform and pointwise polynomial inequalities in regions with cusps in the weighted Lebesgue space, Jaen J. Approx. 7 (2), 231-261, 2015.
  8. F.G. Abdullayev, N.P. Özkartepe, C.D. Gün, Uniform and pointwise polynomial inequalities in regions without cusps in the weighted Lebesgue space, Bulletin of Tbilisi ICMC 18 (1), 146-167, 2014.
  9. L. Ahlfors, Lectures on Quasiconformal Mappings, Princeton, NJ: Van Nostrand, 1966.
  10. V.V. Andrievskii, Weighted Polynomial Inequalities in the Complex Plane, J. Approx. Theory 164(9), 1165-1183, 2012.
  11. V.V. Andrievskii, V.I. Belyi, and V.K. Dzyadyk, Conformal invariants in constructive theory of functions of complex plane, Atlanta: World Federation Publ.Com., 1995.
  12. E. Hille, G. Szegö, and J.D. Tamarkin, On some generalization of a theorem of A. Markoff, Duke Math. 3, 729-739, 1937.
  13. D. Jackson, Certain problems on closest approximations, Bull. Amer. Math. Soc. 39, 889-906, 1933.
  14. O. Lehto and K.I. Virtanen, Quasiconformal Mapping in the Plane, Springer Verlag, Berlin, 1973.
  15. F.D. Lesley, Hölder continuity of conformal mappings at the boundary via the strip method, Indiana Univ. Math. J. 31, 341-354, 1982.
  16. D.I. Mamedhanov, Inequalities of S.M.Nikol’skii type for polynomials in the complex variable on curves, Soviet Math. Dokl. 15, 34-37, 1974.
  17. D.I. Mamedhanov, On Nikol’skii-type inequalities with new characteristic, Dokl. Math. 82, 882-883, 2010.
  18. G.V. Milovanovic, D.S. Mitrinovic, and Th.M. Rassias, Topics in Polynomials: Extremal Problems, Inequalities, Zeros, World Scientific, Singapore, 1994.
  19. S.M. Nikol’skii, Approximation of Function of Several Variable and Imbeding Theorems, Springer-Verlag, New-York, 1975.
  20. N.P. Özkartepe and F.G. Abdullayev, Interference of the weight and boundary contour for algebraic polynomials in the weighted Lebesgue spaces I, Ukr. Math. J. 68(10), 1574-1590, 2017.
  21. Ch. Pommerenke, Univalent Functions, Göttingen, Vandenhoeck & Ruprecht, 1975.
  22. Ch. Pommerenke, Boundary Behavior of Conformal Maps, Springer-Verlag, Berlin, 1992.
  23. I. Pritsker, Comparing Norms of Polynomials in One and Several Variables, J. Math. Anal. Appl. 216, 685-695, 1997.
  24. S. Rickman, Characterisation of quasiconformal arcs, Ann. Acad. Sci. Fenn., Ser. A, Mathematica 395, 30 p, 1966.
  25. G. Szegö and A. Zigmund, On certain mean values of polynomials, J. Anal. Math. 3, 225-244, 1954.
  26. P.K. Suetin, The ordinally comparison of various norms of polynomials in the complex domain, Matematicheskie zapiski Uralskogo Gos. Universiteta 5 (4), 1966 (in Russian).
  27. P.K. Suetin, Main properties of the orthogonal polynomials along a circle, Uspekhi Math. Nauk 21 (2 (128)), 41-88, 1966.
  28. P.K. Suetin, On some estimates of the orthogonal polynomials with singularities weight and contour, Sib. Math. J VIII (3), 1070-1078, 1967 (in Russian).
  29. J.L. Walsh, Interpolation and Approximation by Rational Functions in the Complex Domain, AMS, 1960.
  30. S.E. Warschawski, On differentiability at the boundary in conformal mapping, Proc. Amer. Math. Soc., 12, 614-620, 1961.
  31. G. Szegö and A. Zigmund, On certain mean values of polynomials, J. Anal. Math. 3, 225-244, 1954.