The Smirnov Class for Sub-Bergman Hilbert Spaces

2023/08/01 by Şahin, Sibel
#Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2308.00492

Abstract

In this work we consider the Smirnov classes for sub-Bergman spaces. First we point out some observations about the Smirnov property of sub-Bergman space H^α(φ) and its relation to the defining H^∞₁ function φ. The first main result of the work deals with the range of the defect operator over Smirnov-sub-Bergman class whereas in the last part we show that contrary to classical Bergman spaces, Smirnov-sub-Bergman classes have non-tangential boundary values almost everywhere on the unit circle.

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