Weighted composition operators on the space of bounded harmonic functions (Q649042)

The authors continue the work initiated in [\textit{J. S. Choa}, \textit{K. J. Izuchi} and \textit{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.