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2016•arXiv (Cornell University)Open access

Absolutely summing Carleson embeddings on Hardy spaces

Pascal Lefèvre, Luis Rodrı́guez-Piazza

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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 $\ge$ 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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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 $\ge$ 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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Available 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 $\ge$ 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

Key concepts: Unit disk, Hardy space, Mathematics Subject Classification, Mathematics, Space (punctuation), Measure (data warehouse), Unit (ring theory), Subject (documents)

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