Factorization of Hardy-Orlicz Space on the Disk and applications to Hankel Operators

2025/04/01 by Dje, Jean-Marcel Tanoh, Feuto, Justin
#Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.00830

Abstract

In this work, we prove that the product of a function belonging to a Hardy-Orlicz space H^Φ₁ and a function from another Hardy-Orlicz space H^Φ₂ belongs to a third Hardy-Orlicz space H^Φ₃. Moreover, we establish the converse: any holomorphic function in the space H^Φ₃ can be expressed as the product of two functions, one from H^Φ₁ and the other from H^Φ₂. Subsequently, we use this factorization result in Hardy-Orlicz spaces to study the continuity of the Hankel operator in these spaces. More specifically, we provide gain and loss estimates for the norms of the Hankel operator in the context of analyzing its continuity in Hardy-Orlicz spaces.

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• Hankel operators on holomorphic Hardy-Orlicz spaces
• Hankel Operators and Weak Factorization for Hardy-Orlicz Spaces
• Multipliers for Hardy-Orlicz spaces and applications
• Factorization of some Hardy type spaces of holomorphic functions
• Toeplitz and Hankel operators between distinct Hardy spaces