Majorants in Hardy-Littlewood type theorem for higher order derivatives of analytic functions

• Date: 2013
• Main Authors: Piddubnyĭ, O. M., Savchuk, V. V., Піддубний, О. М., Савчук, В. В.
• Format: Article
• Language: Ukrainian
• Published: Інститут математики НАН України 2013
• Online Access: https://trim.imath.kiev.ua/index.php/trim/article/view/163
• Journal Title: Transactions of Institute of Mathematics of NAS of Ukraine

We study the classes $\mathop{\rm Lip}_\lambda(\mathbb D)$, $\mathscr L_\lambda^k$ and $\mathscr B_\lambda^k,$ $k\in\mathbb N,$ consisting of analytic functions $f$ for which respectively $|f(z_1)-f(z_2)|=O(|z_1-z_2|)$, $|f^{(k)} z)|=O(|\lambda^{(k)}(1-|z|)|)$ and $|f^{(k)}(z)|=O(\lambda(1-|z|)/(1-|...