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

Abstract

Let µ be a positive Borel measure on the interval [0, 1). The Hankel matrixa n z n is an analytic function in D, the Hilbert operator is defined byThe Derivative-Hilbert operator is defined asIn this paper, we determine the range of the Hilbert operator and Derivative-Hilbert operator acting on H ∞ .