2022-12-03T12:52:43Zhttps://soar-ir.repo.nii.ac.jp/oaioai:soar-ir.repo.nii.ac.jp:000120062022-06-29T02:20:14ZOn a theorem of MacCluer and ShapiroMatsugu, YNagai, SUeki, SLet μ be a holomorphic function in the unit ball B of C^n and φ be a univalent holomorphic self-map of B. We give some sufficient conditions for μ and φ that the weighted composition operator μC_φ is bounded or compact on the Hardy spaces H^p(B) and the weighted Bergman spaces A^p(v_a) (0<p<∞,-1<α<∞). This our result is a generalization of a theorem of B. D. MacCluer and J. H. Shapiro [9] concerning the composition operator C_φ. And we also give similar sufficient conditions for such operator to be metrically bounded or metrically compact on the Privalov spaces N^p(B) (1<p<∞) and the weighted Bergman-Privalov spaces (AN)^p (v_a) (1≤p<∞, -1<α<∞).ArticleJournal of the Faculty of Science Shinshu University 40:1-26(2006)departmental bulletin paper信州大学理学部2006-03-24application/pdfJournal of the Faculty of Science Shinshu University401260583-063XAA00697923https://soar-ir.repo.nii.ac.jp/record/12006/files/KJ00004361935.pdfeng