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Weighted composition operators from F(p,q,s) into logarithmic Bloch space. (English) Zbl 1156.47031
For analytic functions u,f on the open unit disk D and an analytic mapping φ:DD, define the weighted composition operator uC φ by (uC φ f)(z)=u(z)f(φ(z)). The aim of the present paper is to characterize those u and φ for which the corresponding weighted composition operator uC φ maps the space F(p,q,s) into the logarithmic Bloch space B L , those u and φ for which it maps F 0 (p,q,s) into B L 0 , and finally those u and φ for which the corresponding map is compact. The spaces F(p,q,s) were introduced by R.–H. Zhao [“On a general family of function spaces” (Ann. Acad. Sci. Fenn., Math., Diss. 105; Helsinki: Suomalainen Tiedeakatemia) (1996; Zbl 0851.30017)].
47B33Composition operators
30H05Bounded analytic functions