tailieunhanh - Báo cáo hóa học: " Research Article Integral-Type Operators from F p, q, s Spaces to Zygmund-Type Spaces on the Unit Ball Congli Yang1, 2"

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 Integral-Type Operators from F p, q, s Spaces to Zygmund-Type Spaces on the Unit Ball Congli Yang1, 2 | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 789285 14 pages doi 2010 789285 Research Article Integral-Type Operators from F p q s Spaces to Zygmund-Type Spaces on the Unit Ball Congli Yang1 2 1 Department of Mathematics and Computer Science Guizhou Normal University 550001 Gui Yang China 2 Department of Physics and Mathematics University of Eastern Finland . Box 111 80101 Joensuu Finland Correspondence should be addressed to Congli Yang Received 7 May 2010 Revised 21 September 2010 Accepted 23 December 2010 Academic Editor Siegfried Carl Copyright 2010 Congli Yang. 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. Let H B denote the space of all holomorphic functions on the unit ball B c Cn. This paper investigates the following integral-type operator with symbol g e H B Tgf z J1 f fz Rg fz df t f e H B z e B where Rg z n 1 Zjdg dzj z is the radial derivative of g. We characterize the boundedness and compactness of the integral-type operators Tg from general function spaces F p q s to Zygmund-type spaces Zp where p is normal function on 0 1 . 1. Introduction Let B be the open unit ball of Cn let ÔB be its boundary and let H B be the family of all holomorphic functions on B. Let z z1 . zn and w w1 . wn be points in Cn and z w z1w1 znwn. Let n df Rf z s zidz z stand for the radial derivative of f e H B . For a e B let g z a log 1 a z where ya is the Mobius transformation of B satisfying a 0 a ya a 0 and pa ự-1. For 0 p s TO -n - 1 q TO we say f e F p q s provided that f e H B and f F p q s f 0 p suP lRf z p0 - z 2Ỵg z a dv z TO. 2 Journal of Inequalities and Applications The space F p q s introduced by Zhao in 1 is known as the general family of function spaces. For appropriate parameter values p q and s F p q s coincides