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Weighted composition operators on the space of bounded harmonic functions. (English) Zbl 1241.47023

The authors continue the work initiated in [J. S. Choa, K. J. Izuchi and S. Ohno, “Composition operators on the space of bounded harmonic functions”, Integral Equations Oper. Theory 61, No. 2, 167–186 (2008; Zbl 1155.47027)], where compactness and boundedness of weighted composition operators defined on \(h^\infty(\mathbb D)\) were characterized and, moreover, the essential norm of the differences of two composition operators on \(h^\infty(\mathbb D)\) was considered.
In the paper under review, the value of the essential norm of weighted composition operators and differences between them acting on \(h^\infty\) are determined. The main issue of the paper is to work at the boundary rather than inside the disc and, for that purpose, the authors make a detailed study of some properties of functions in \(L^\infty(\mathbb T)\) which they need for their considerations.

MSC:

47B33 Linear composition operators
47B38 Linear operators on function spaces (general)
30H10 Hardy spaces

Citations:

Zbl 1155.47027
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References:

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