Optimal universal growth for integral means of normalized logarithmic derivatives in the Carath\'eodory class
Yixin He, Quanyu Tang, Teng Zhang
TL;DR
This paper establishes the best possible growth bounds for integral means of normalized logarithmic derivatives within the Carathéodory class, solving a longstanding problem.
Contribution
It provides the first precise determination of the optimal universal growth scale for these integral means, addressing a problem posed by D. K. Thomas.
Findings
Identified the exact growth scale for integral means in the Carathéodory class
Resolved D. K. Thomas's open problem on growth bounds
Established a benchmark for future research in geometric function theory
Abstract
We determine the optimal universal growth scale for the integral means of normalized logarithmic derivatives in the Carath\'eodory class. This resolves a problem of D.~K.~Thomas.
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Taxonomy
TopicsMeromorphic and Entire Functions · Holomorphic and Operator Theory · Analytic and geometric function theory