Báo cáo hóa học: " Research Article Isometries on Products of Composition and Integral Operators on Bloch Type Space"

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 Isometries on Products of Composition and Integral Operators on Bloch Type Space | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 184957 9 pages doi 2010 184957 Research Article Isometries on Products of Composition and Integral Operators on Bloch Type Space Geng-Lei Li1 2 and Ze-Hua Zhou1 1 Department of Mathematics Tianjin University Tianjin 300072 China 2 Department of Mathematics Tianjin Polytechnic University Tianjin 300160 China Correspondence should be addressed to Ze-Hua Zhou zehuazhou2003@ Received 8 June 2010 Accepted 12 July 2010 Academic Editor Jozef Banas Copyright 2010 . Li and . Zhou. 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. We characterize the isometries on the products of composition and integral operators on the Bloch type space in the disk. 1. Introduction Let D be the unit disk of the complex plane and S D be the set of analytic self-maps of D. The algebra of all holomorphic functions with domain D will be denoted by H D . We recall that the Bloch type space Ba a 0 consists of all f e H D such that Ilf Ik sup 1 - z 2 a f z k1 zeD then II Ba is a complete seminorm on Ba which is Mobius invariant. It is well known that Ba is a Banach space under the norm Ilf II f 0 lfllBa. Let p be an analytic self-map of D then the composition operator Cv induced by p is defined by Cf z f y z for z e D andf e H D . 2 Journal of Inequalities and Applications Let g e H D then the integer operator Ig is defined by f z Igf z f g dl z e D 0 for f e H D . The products of composition and integral type operators were first introduced and discussed by Li and Stevic 1-3 which are defined by Cyigf z r z f g dt 0 igCyf z r f ỳ g dị. 0 Let X and Y be two Banach spaces recall that a linear isometry is a linear operator T from X to Y such that Tf Y f X for all f e X. In 4 Banach raised the question .

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