Carleson embedding theorem for an exponential Bergman space on the unit ball

TL;DR

This paper characterizes Carleson measures for an exponential Bergman space on the unit ball in complex space, linking measure properties to operator boundedness and compactness.

Contribution

It provides a new characterization of Carleson measures for exponential Bergman spaces using the complex Hessian of the weight function.

Findings

Characterization of Carleson measures via complex Hessian

Criteria for boundedness of integral, Cesàro, and Toeplitz operators

Conditions for operator compactness based on Carleson measures

Abstract

We characterize the Carleson measures for an exponential Bergman space on the unit ball of $\mathbb C^n$ in terms of the ball induced by the complex Hessian of the logarithm of the weight function. The boundedness (or compactness) of integral operators, Ces\`{a}ro operators and Toeplitz operators, is given using the Carleson measure (or vanishing Carleson measure) characterization.