Carleson and reverse Carleson measures on homogeneous Siegel domains

TL;DR

This paper investigates conditions under which measures are Carleson or reverse Carleson for holomorphic function spaces on homogeneous Siegel domains, providing necessary and sufficient criteria for these measures.

Contribution

It establishes new necessary and sufficient conditions for Carleson and reverse Carleson measures on mixed-normed weighted Bergman spaces on homogeneous Siegel domains.

Findings

Derived necessary conditions for Carleson measures.

Established sufficient conditions for reverse Carleson measures.

Characterized measures for holomorphic function spaces on Siegel domains.

Abstract

In this paper we study Carleson and reverse Carleson measures on holomorphic function spaces on a homogeneous Siegel domain of Type II. We prove several necessary conditions and sufficient conditions in order for a measure $\mu$ to be Carleson and reverse Carleson on mixed-normed weighted Bergman spaces.