Compact Carleson measures from sparse sequences

TL;DR

This paper investigates the characterization of compact Carleson measures for specific analytic function spaces, extending previous work on general Carleson measures to the compact case, with implications for de Branges and Hardy space subspaces.

Contribution

It provides a new analysis of compact Carleson measures for de Branges and model subspaces of Hardy spaces, advancing understanding of their measure-theoretic properties.

Findings

Characterization of compact Carleson measures for de Branges spaces

Extension of Carleson measure theory to the compact case

New criteria for measure compactness in analytic function spaces

Abstract

In [1], Y. Belov, K. Seip, and the author studied the Carleson measures for certain spaces of analytic functions of which the de Branges spaces and the model subspaces of the Hardy space H2 are the prime examples. In this paper, we continue this line of research by studying the compact Carleson measures for such spaces.