On the Bohr inequality for the Cesáro operator

Abstract

We investigate an analog of Bohr’s results for the Cesáro operator acting on the space of holomorphic functions defined on the unit disk. The asymptotical behaviour of the corresponding Bohr sum is also estimated. 2020 Mathematics Subject Classification. 30H05, 30A10, 30C80. Funding. The work of I. Kayumov and D. Khammatova is supported by the Russian Science Foundation under grant 18-11-00115. The work of the third author is supported by Mathematical Research Impact Centric Support of DST, India (MTR/2017/000367). Manuscript received 1st January 2019, revised and accepted 26th May 2020.