Order boundedness of weighted composition operators between two classes of function spaces. (Chinese. English summary) Zbl 1504.47046
Summary: In this paper, we first investigate the correspondence between order boundedness and Hilbert-Schmidt of weighted composition operators \(W_{\phi,\varphi}(f) := \phi f \circ \varphi\). Then, by resorting to the estimates of the norms of point evaluation functionals \(\delta_z\) and derivative point evaluation functionals \(\delta_z'\) on weighted Dirichlet spaces \(D_\beta^q\) (\(0<q<\infty\), \(- 1 < \beta < \infty\)) and derivative Hardy spaces \(S^p\) (\(0<p<\infty\)), the order boundedness of weighted composition operators \(W_{\phi,\varphi}\) between weighted Dirichlet spaces \(D_\beta^q\) and derivative Hardy spaces \(S^p\) are completely characterized.
MSC:
| 47B33 | Linear composition operators |
| 30H05 | Spaces of bounded analytic functions of one complex variable |
Keywords:
weighted Dirichlet space; derivative Hardy space; weighted composition operator; order boundednessReferences:
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