Embeddings of vector-valued Bergman spaces

TL;DR

This paper extends the Carleson embedding theorem to vector-valued Bergman spaces and discusses related embeddings for analytic vector-valued functions, highlighting differences from Hardy space results.

Contribution

It introduces a dyadic version of the Carleson embedding theorem for vector-valued Bergman spaces and explores new embeddings for analytic vector-valued functions.

Findings

Dyadic Carleson embedding theorem extends to vector-valued Bergman spaces.

Contrasts with Hardy space results by Nazarov, Treil, Volberg.

Discusses embeddings for analytic vector-valued functions.

Abstract

We remark that a dyadic version of the Carleson embedding theorem for the Bergman space extends to vector-valued functions and operator-valued measures. This is in contrast to a result by Nazarov, Treil, Volberg in the context of the Hardy space. We also discuss some embeddings for analytic vector-valued functions.