Нерiвностi типу Маркова–Нiкольського в областях iз внутрiшнiми нульовими кутами в просторi Бергмана

Пелiн  Озкартепе

doi:10.37863/umzh.v75i3.7322

Пелiн Озкартепе Газiантепський унiверситет, Туреччина

DOI: https://doi.org/10.37863/umzh.v75i3.7322

Ключові слова: Markov inequality, Nikolskii inequality, Algebraic polynomials, Conformal mapping, Smooth curve

Анотація

УДК 517.5

Досліджується порядок зростання модуля довільного алгебраїчного полінома у ваговому просторі Бергмана $A_{p}(G,h),$ $p>0,$ в областях, що мають зовнішні ненульові та внутрішні нульові кути у скінченному числі точок межі. Отримано оцінки типу Маркова–Нікольського для алгебраїчних поліномів, а також з'ясовано поведінку похідних поліномів у точках нулів і полюсів вагової функції в обмежених областях з кусково-гладкою межею.

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