Absolutely summing Carleson embeddings on Hardy spaces

TL;DR

This paper characterizes absolutely summing Carleson embeddings of Hardy spaces into Lp spaces with respect to Carleson measures, extending previous results and solving a long-standing open problem in operator theory.

Contribution

It provides a complete characterization of r-summing Carleson embeddings on Hardy spaces for p > 1, advancing the understanding of these operators and their summing properties.

Findings

Characterization of r-summing Carleson embeddings on Hardy spaces.

Extension of classical results to a broader class of operators.

Resolution of an open problem from the 1970s.

Abstract

We consider the Carleson embeddings of the classical Hardy spaces (on the disk) into a L p ($\mu$) space, where $\mu$ 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