Absolutely summing Carleson embeddings on Hardy spaces

2016/10/07 by Pascal Lefèvre, Lefèvre, Pascal, Luis Rodrı́guez-Piazza +1 · 3 citations
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · doi:10.48550/arxiv.1610.02246

openalex publication_date 2016/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the Carleson embeddings of the classical Hardy spaces (on the disk) into a L p (μ) space, where μ is a Carleson measure on the unit disk. This includes the case of composition operators. We characterize such operators which are r-summing on H p , where p \textgreater 1 and r ≥ 1. This completely extends the former results on the subject and solves a problem open since the early seventies. Mathematics Subject Classification. Primary: 47B33 -- Secondary: 28A12; 30C85; 31A15; 46E20; 46E22; 47B06

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• Absolutely summing Hankel operators on Bergman spaces
• Summing Carleson measure on radial weighted Begman spaces
• Absolutely Summing Toeplitz operators on Fock spaces

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