Volume 11 • Issue 1 • PP: 47-53 • 2024
On The Markov-Bernstein Inequalities with Weight Functions in Lp Spaces
Abstract
In this paper, we study of the Markov- Bernstein inequality of a complex polynomial with exponential weight functions e^(-r^2 z/2) on the domain ├]-∞,+∞┤[, we also study the Integral Markov-Bernstein inequality for the algebraic polynomials of degree 2m and degree m with algebraic weight functions on the domain [1,+∞┤[of type (1/x^2 )^(-n), and on the domain ├]0,+∞┤[of type (1/t)^(-n).
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References
[1] L. Lukashov, Inequalities for the derivatives of rational functions on several intervals. Izv. Ross. Akad. Nauk Ser. Mat., 68(2004), 115–138,(Russian); English translation in Izv. Math., 68(2004), 543 565.
[2] Serge kalmykov Be`la Nagy and Vilmos Totik, Bernestein- and Markov-Type inequalities, arxiv: 2014.0234V2 (math.ev) 21 May2021.
[3] GUVEN.A; ISRAFILOV, D-M. Multiplier Theorems in Weighted smirnov space. J.Korean Math Soc, 45, No 6, 2008, 1535-1548.
[4] T.Kilgore, Inter polation properties of polynomial of degree at most 2n Weighted by
[5] T.Kilgore, Markov and Bernstien inequalities in Lp for some Weighted algebraic and trigonometric poly mails, Journal of Inequalities and Application.4 (2005), 413-321.
[6] V. Totik, Bernstein and Markov type inequalities for trigonometric polynomials on general sets. Int. Math. Res. Not., IMRN, 11(2015), 2986–3020.
[7] Nagy and F. To´okos, Bernstein inequality in Lα norms. Acta Sci.Math. (Szeged), 79(2013), 129–174.
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