Riemann-Stieltjes operators and multipliers on $Q_p$ spaces in the unit ball of $C^n$

TL;DR

This paper characterizes Riemann-Stieltjes operators and multipliers on $Q_p$ spaces in the unit ball of $C^n$, establishing boundedness and compactness criteria via embeddings into non-isotropic tent spaces.

Contribution

It provides a comprehensive characterization of operators on $Q_p$ spaces, unifying BMOA and Bloch space, and links their boundedness to embeddings into tent spaces.

Findings

Boundedness of operators characterized by embeddings.

Compactness criteria established for Riemann-Stieltjes operators.

Unified framework for BMOA and Bloch space in $Q_p$ spaces.

Abstract

This paper is devoted to characterizing the Riemann-Stieltjes operators and pointwise multipliers acting on M${\rm \ddot{o}}$bius invariant spaces $Q_p$, which unify BMOA and Bloch space in the scale of $p$. The boundedness and compactness of these operators on $Q_p$ spaces are determined by means of an embedding theorem, i.e. $Q_p$ spaces boundedly embedded in the non-isotropic tent type spaces $T_q^\infty$.