Carleson measures and the range of a Ces\`aro-like operator acting on $H^\infty$

TL;DR

This paper characterizes Carleson measures on [0,1) to determine the range of a Cesàro-like operator on H-infinity, addressing a recent question and expanding understanding of operator ranges in complex analysis.

Contribution

It provides new characterizations of Carleson measures and explicitly determines the operator's range, solving a problem posed by Galanopoulos, Girela, and Merchán.

Findings

Characterizations of Carleson measures on [0,1)

Range of Cesàro-like operator on H-infinity determined

Answer to a recent open question in the field

Abstract

In this paper, by describing characterizations of Carleson type measures on $[0,1)$, we determine the range of a Ces\`aro-like operator acting on $H^\infty$. A special case of our result gives an answer to a question posed by P. Galanopoulos, D. Girela and N. Merch\'an recently.