Illinois Journal of Mathematics

Hausdorff matrices and composition operators

Petros Galanopoulos and Aristomenis G. Siskakis

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Abstract

We consider Hausdorff matrices as operators on Hardy spaces of analytic functions. When the generating sequence of the matrix is the moment sequence of a measure $\mu$, we find conditions on $\mu$ such that the matrix represents a bounded operator. The results unify and extend some known special cases of operators on Hardy spaces such as the Cesàro and generalized Cesàro operators.

Article information

Source
Illinois J. Math., Volume 45, Number 3 (2001), 757-773.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138149

Digital Object Identifier
doi:10.1215/ijm/1258138149

Mathematical Reviews number (MathSciNet)
MR1879233

Zentralblatt MATH identifier
0994.47026

Subjects
Primary: 47B33: Composition operators
Secondary: 30D55 40G05: Cesàro, Euler, Nörlund and Hausdorff methods 46E15: Banach spaces of continuous, differentiable or analytic functions 47A57: Operator methods in interpolation, moment and extension problems [See also 30E05, 42A70, 42A82, 44A60]

Citation

Galanopoulos, Petros; Siskakis, Aristomenis G. Hausdorff matrices and composition operators. Illinois J. Math. 45 (2001), no. 3, 757--773. doi:10.1215/ijm/1258138149. https://projecteuclid.org/euclid.ijm/1258138149


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