Carleson measures, Riemann-Stieltjes and multiplication operators on a general family of function spaces

TL;DR

This paper characterizes measures for which a broad class of analytic function spaces are boundedly or compactly embedded into tent-type spaces, and applies these results to Riemann-Stieltjes and multiplication operators.

Contribution

It provides a comprehensive characterization of measures ensuring bounded and compact embeddings of $F(p,q,s)$ spaces into tent spaces, and analyzes operator boundedness and compactness.

Findings

Characterization of measures for bounded/compact embeddings

Criteria for boundedness of Riemann-Stieltjes operators

Criteria for boundedness of multiplication operators

Abstract

Let $\mu$ be a nonnegative Borel measure on the unit disk of the complex plane. We characterize those measures $\mu$ such that the general family of spaces of analytic functions, $F(p,q,s)$, which contain many classical function spaces, including the Bloch space, $BMOA$ and the $Q_s$ spaces, are embedded boundedly or compactly into the tent-type spaces $T^{\infty}_{p,s}(\mu)$. The results are applied to characterize boundedness and compactness of Riemann-Stieltjes operators and multiplication operators on $F(p,q,s)$.