tailieunhanh - Báo cáo hóa học: " Research Article Weighted Composition Operators between Mixed Norm Spaces ∞ and Hα Spaces in the Unit Ball"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Weighted Composition Operators between Mixed Norm Spaces ∞ and Hα Spaces in the Unit Ball | Hindawi Publishing Corporation Journal ofInequalities and Applications Volume 2007 Article ID 28629 9 pages doi 2007 28629 Research Article Weighted Composition Operators between Mixed Norm Spaces and HTO Spaces in the Unit Ball Stevo Stevic Received 15 March 2007 Accepted 1 November 2007 Recommended by Ulrich Abel Let y be an analytic self-map and let u be a fixed analytic function on the open unit ball B in C . The boundedness and compactness of the weighted composition operator uCyf u f y between mixed norm spaces and HTO are studied. Copyright 2007 Stevo Stevic. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction Let B be the open unit ball in C dB S its boundary D the unit disk in C dV the normalized Lebesgue volume measure on B dơ the normalized surface measure on S and H B the class of all functions analytic on B. An analytic self-map y B B induces the composition operator Cy on H B defined by Cy f z f y z for f e H B . It is interesting to provide a functional theoretic characterization of when y induces a bounded or compact composition operator on various spaces. The book 1 contains a plenty of information on this topic. Let u be a fixed analytic function on the open unit ball. Define a linear operator uCy called a weighted composition operator by uCyf u f o y where f is an analytic function on B. We can regard this operator as a generalization of the multiplication operator Mu f uf and a composition operator. A positive continuous function Ộ on 0 1 is called normal if there exist numbers s and t 0 s t such that ộ r 1 - r s decreasingly converges to zero and ộ r 1 - ry increasingly tends to TO as r 1 see . 2 . For 0 p TO 0 q TO and a normal function Ộ let H p q Ộ denote the space of all f e H B such that 2 Journal of Inequalities and Applications f1 D r fp r p II f H p q Mq

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