Exact constants in inequalities for the Taylor coefficients of bounded holomorphic functions in a polydisc

• Date: 2015
• Main Authors: Meremelya, I. Yu., Savchuk, V. V., Меремеля, І. Ю., Савчук, В. В.
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2015
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2101
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We determine the exact constants $L_{m,n}(X)$ in the inequalities of the form $|\hat f(m)|\leq L_{m,n}(X)(1 − |\hat f(n)|)$ for the pairs of Taylor coefficients $\hat f(m)$ and $\hat f(n)$ on some classes $X$ of bounded holomorphic functions in a polydisc.