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Bernstein-Walsh-Type Polynomial Inequalities in Domains Bounded by Piecewise Asymptotically Conformal Curve with Nonzero Inner Angles in the Bergman Space

Fahreddin ABDULLAYEV | Dağıstan ŞİMŞEK

We continue our investigation of the order of growth of the modulus of an arbitrary algebraic polynomial in the Bergman weight space, where the contour and weight functions have certain singularities. In particular, we deduce a Bernstein-Walsh-type pointwise estimate for algebraic polynomials in unbounded domains with piecewise asymptotically conformal curves with nonzero inner angles in the Bergman weight space.

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Polynomial Inequalities in Regions with Zero Interior Angles in the Bergman Space

Sebahattin BALCI | Meerim İmaş Kızı | Fahreddin ABDULLAYEV

We study the order of growth of the moduli of arbitrary algebraic polynomials in the weighted Bergman space A(p)(G, h), p > 0, in regions with zero interior angles at finitely many boundary points. We obtain estimates for algebraic polynomials in bounded regions with piecewise smooth boundary.

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Bernstein-Nikol'skii-Type Inequalities for Algebraic Polynomials from the Bergman Space in Domains of the Complex Plane

Fahreddin ABDULLAYEV

We study Bernstein-type and Nikol'skii-type estimates for an arbitrary algebraic polynomial in regions of the complex plane.

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