On a theorem of MacCluer and Shapiro

概要

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Let 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<∞).
信州大学の論文
2006-03-24