Classical and new loglog-theorems
Alexander Rashkovskii
TL;DR
This paper introduces integral variants of classical theorems on analytic function majorants, utilizing harmonic measure projections of star-shaped domains to extend existing results in complex analysis.
Contribution
It provides a new integral framework for classical loglog-theorems, expanding their applicability through geometric and harmonic measure techniques.
Findings
Derived integral variants of classical theorems.
Complete description of radial projections of harmonic measures.
Extended the scope of loglog-theorems in complex analysis.
Abstract
We present integral variants of results due to Carleman, Wolf, Levinson, Sjoberg, and Matsaev on majorants of analytic functions. Main ingredient is a complete description for radial projections of harmonic measures of strictly star-shaped domains in the plane.
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Taxonomy
TopicsAnalytic and geometric function theory · Holomorphic and Operator Theory · Algebraic and Geometric Analysis