Bernstein-Nikol’skii-Markov-type inequalities for algebraic polynomials in aweighted Lebesgue space in regions with cusps

Authors

UĞUR DEĞERFollow
FAHREDDİN ABDULLAYEVFollow

Author ORCID Identifier

FAHREDDİN ABDULLAYEV: 0000-0002-9711-0796

UĞUR DEĞER: 0000-0002-1741-1178

DOI

10.55730/1300-0098.3536

Abstract

In this paper, we study Bernstein-Nikol’skii-Markov type inequalities for arbitrary algebraic polynomials withrespect to a weighted Lebesgue space, where the weight functions have some singularities on a given contour. We considercurves which can contain a finite number of exterior and interior corners with power law tangency of the boundary arcs atthose points where the weight functions have both zeros and poles of finite order. The estimates are given for the growthof the module of derivatives for algebraic polynomials on the closure of a region bounded by a given curve, dependingon the behavior of weight functions, on the property of curve, and on the degree of contact of the boundary arcs, whichform zero angles on the boundary.

Keywords

Algebraic polynomials, conformal mapping, quasicircle

First Page

713

Last Page

733

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Recommended Citation

DEĞER, UĞUR and ABDULLAYEV, FAHREDDİN (2024) "Bernstein-Nikol’skii-Markov-type inequalities for algebraic polynomials in aweighted Lebesgue space in regions with cusps," Turkish Journal of Mathematics: Vol. 48: No. 4, Article 7. https://doi.org/10.55730/1300-0098.3536
Available at: https://journals.tubitak.gov.tr/math/vol48/iss4/7