On The Markov-Bernstein Inequalities with Weight Functions in Lp Spaces

Sergey Drominko; Erina Kovachiskaya

doi:https://doi.org/10.54216/GJMSA.0110105

On The Markov-Bernstein Inequalities with Weight Functions in Lp Spaces

Sergey Drominko ^{1
*} , Erina Kovachiskaya ²

1 Faculty of Information Technology and Robotics, Vitebsk State Technological University, Belarus - (Serdrominko1996@vsu.by)

2 Faculty of Information Technology and Robotics, Vitebsk State Technological University, Belarus - (EriKovachi98rus@vsu.by)

Doi: https://doi.org/10.54216/GJMSA.0110105

Received: October 27, 2023 Revised: March 02, 2024 Accepted: June 29, 2024

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).

Keywords :

Markov &ndash , Bernstein inequality , weight functions , Weight Space , Lp-space

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.

Cite This Article As :

Drominko, Sergey. , Kovachiskaya, Erina. On The Markov-Bernstein Inequalities with Weight Functions in Lp Spaces. Galoitica: Journal of Mathematical Structures and Applications, vol. , no. , 2024, pp. 47-53. DOI: https://doi.org/10.54216/GJMSA.0110105

Drominko, S. Kovachiskaya, E. (2024). On The Markov-Bernstein Inequalities with Weight Functions in Lp Spaces. Galoitica: Journal of Mathematical Structures and Applications, (), 47-53. DOI: https://doi.org/10.54216/GJMSA.0110105

Drominko, Sergey. Kovachiskaya, Erina. On The Markov-Bernstein Inequalities with Weight Functions in Lp Spaces. Galoitica: Journal of Mathematical Structures and Applications , no. (2024): 47-53. DOI: https://doi.org/10.54216/GJMSA.0110105

Drominko, S. , Kovachiskaya, E. (2024) . On The Markov-Bernstein Inequalities with Weight Functions in Lp Spaces. Galoitica: Journal of Mathematical Structures and Applications , () , 47-53 . DOI: https://doi.org/10.54216/GJMSA.0110105

Drominko S. , Kovachiskaya E. [2024]. On The Markov-Bernstein Inequalities with Weight Functions in Lp Spaces. Galoitica: Journal of Mathematical Structures and Applications. (): 47-53. DOI: https://doi.org/10.54216/GJMSA.0110105

Drominko, S. Kovachiskaya, E. "On The Markov-Bernstein Inequalities with Weight Functions in Lp Spaces," Galoitica: Journal of Mathematical Structures and Applications, vol. , no. , pp. 47-53, 2024. DOI: https://doi.org/10.54216/GJMSA.0110105

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On The Markov-Bernstein Inequalities with Weight Functions in Lp Spaces

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