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

Abstract

In this paper, by describing characterizations of Carleson type measures on [0, 1), we determine the range of a Cesàro-like operator acting on H ∞ . A special case of our result gives an answer to a question posed by P. Galanopoulos, D. Girela and N. Merchán recently.

The range of Hilbert operator and Derivative-Hilbert operator acting on $H^1$

“…A number of results will be needed to prove our main theorems. We start with a characterization of Carleson measure on [0, 1) see [6] for the detail process of proof. Lemma 3.1.…”

“…They did the similar researches on Bergman spaces in [19]. In [6], Bao and Wulan gave another description about Carleson measure on [0, 1) and proved that when 0 < p < 2, the range of the cesàro-like operator acting on H ∞ is a subset of Q p if and only if µ is a Carleson measure.…”

“…Following the idea of the paper by Bao and Wulan [6], In this paper, we determine the range of the Hilbert operator and Derivative-Hilbert operator acting on H ∞ .…”