Order boundedness of weighted composition operators on weighted Dirichlet spaces and derivative Hardy spaces. (English) Zbl 1486.47048
Order boundedness of weighted composition operators \(W_{\phi,\varphi}\) between weighted Dirichlet spaces \(D_{\alpha}^p\) and \(D_{\beta}^q\), \(p,q>0\), \(\alpha,\beta>-1\) (Theorem 1) and derivative Hardy spaces \(S^p\) and \(S^q\), \(p,q>0\) (Theorem 2) is characterized.
Theorem 1 was proved for \(\alpha=p-1\) and \(\beta=q-1\) in [Y. Gao et al., Chin. Ann. Math., Ser. B 37, No. 4, 585–594 (2016; Zbl 1362.47008)] and [A. K. Sharma, Positivity 21, No. 3, 1213–1221 (2017; Zbl 1439.47024)].
Theorem 1 was proved for \(\alpha=p-1\) and \(\beta=q-1\) in [Y. Gao et al., Chin. Ann. Math., Ser. B 37, No. 4, 585–594 (2016; Zbl 1362.47008)] and [A. K. Sharma, Positivity 21, No. 3, 1213–1221 (2017; Zbl 1439.47024)].
Reviewer: Shamil Makhmutov (Muscat)
MSC:
| 47B33 | Linear composition operators |
| 30H05 | Spaces of bounded analytic functions of one complex variable |
| 30H25 | Besov spaces and \(Q_p\)-spaces |
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