tailieunhanh - Báo cáo hóa học: " Research Article Riemann-Stieltjes Operators between Vector-Valued Weighted Bloch Spaces"

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 Riemann-Stieltjes Operators between Vector-Valued Weighted Bloch Spaces | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008 Article ID 348208 15 pages doi 2008 348208 Research Article Riemann-Stieltjes Operators between Vector-Valued Weighted Bloch Spaces Maofa Wang School of Mathematics and Statistics Wuhan University Wuhan 430072 China Correspondence should be addressed to Maofa Wang Received 6 June 2008 Revised 1 August 2008 Accepted 11 September 2008 Recommended by Jozsef Szabados Let X be a Banach space we study Riemann-Stieltjes operators between X-valued weighted Bloch spaces. Some necessary and sufficient conditions for these operators induced by holomorphic functions to be weakly compact and weakly conditionally compact are given by certain growth properties of the inducing symbols and some structural properties of the abstract Banach space which extend some previous results. Copyright 2008 Maofa Wang. 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 and statement of the main results Let D z e C z 1 be the open unit disk in the complex plane C. Denote by H D the space of all holomorphic functions on D. For g e H D the Riemann-Stieltjes operator Tg is defined on H D by f z f 1 Tgf z f f ftz zg ftz dt z e D. M 0 0 The Riemann-Stieltjes operator Tg can be viewed as a generalization of the well-known Cesaro operator defined by 1 rz f n 1 n C fixz if gtj-nVV zeD L2 for f z Zn anZn e H D . Pommerenke 1 initiated the study of Riemann-Stieltjes operators on Hardy space H2 where he proved that Tg is bounded on H2 if and only if g is in BMOA the space of 2 Journal of Inequalities and Applications holomorphic functions on D with bounded mean oscillation. This result later was extended to other Hardy spaces Hp 1 p TO see 2 . Similar questions on weighted Bergman spaces were considered by Aleman and .