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September 22, 2026
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Регулярность границ неванлинновских областей и однолистные функции в модельных подпространствах

Математический сборник. 2011. № 12. С. 3–22.
Baranov A., Федоровский К. Ю.
Language: Russian
Keywords: внутренняя функцияневанлинновская областьмодельное подпространствоконформное отображениепроизведение Бляшке
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Let p⁡(ζ) be a positive function defined on the unit circle T and satisfying the condition|p⁡(ζ2)−p⁡(ζ1)|≤c0log⁡e|ζ2−ζ1|,ζ1,ζ2∈T,p−=minζ∈T⁡p⁡(ζ). Futhermore, let 0<α<1, r≥0, r∈Z, and assume that p−>1α. Define a class of analytic functions in the unit disk D as follows: f∈Hr+αp⁡(⋅) ifsup0<ρ<1⁡sup0<|θ|<π⁡∫02⁢π|f(r)⁡(ρ⁢ei⁢(λ+θ))−f(r)⁡(ρ⁢ei⁢λ)|θ|α|p(ei⁢λ)dλ<∞.The following main results are proved. Theorem 1. Let f∈Hr+αp⁡(⋅), and let I be an inner function, f/I∈H1. Then f/I∈Hr+αp⁡(⋅). Theorem 2. Let f∈Hr+αp⁡(⋅), and let I be an inner function, f/I∈H∞. Assume that the multiplicity of every zero of f in D is at least r+1. Then f⁢I∈Hr+αp⁡(⋅). ...
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