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Báo cáo hóa học: " Research Article ¨ A Note on Holder Type Inequality for the Fermionic p-Adic Invariant q-Integral"

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 ¨ A Note on Holder Type Inequality for the Fermionic p-Adic Invariant q-Integral | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 357349 5 pages doi 10.1155 2009 357349 Research Article A Note on Holder Type Inequality for the Fermionic p-Adic Invariant q-Integral Lee-Chae Jang Department of Mathematics and Computer Science KonKuk University Chungju 380-701 South Korea Correspondence should be addressed to Lee-Chae Jang leechae.jang@kku.ac.kr Received 11 February 2009 Accepted 22 April 2009 Recommended by Kunquan Lan The purpose of this paper is to find Holder type inequality for the fermionic p-adic invariant q-integral which was defined by Kim 2008 . Copyright 2009 Lee-Chae Jang. 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 p be a fixed odd prime. Throughout this paper Zp Qp Q C and Cp will respectively denote the ring of p-adic rational integers the field of p-adic rational numbers the rational number field the complex number field and the completion of algebraic closure of Qp. For a fixed positive integer d with p d 1 let X Xd lim Z dpN Z X1 Zp N X c a dp Zp 0 a dp a p 1 1.1 a dpNZp Ịx e X x a mod dpN Ị where a e Z lies in 0 a dpN cf. 1-24 . Let N be the set of natural numbers. In this paper we assume that q e Cp with 1 - q p p-1 p-1 which implies that qx exp x log q for p p 1. We also use the notations x q 1 - qx x -q 1 - - x 1 q 1.2 2 Journal of Inequalities and Applications for all x e Zp. For any positive integer N the distribution is defined by dq a dpN Zp Jd -. 1.3 We say that f is a uniformly differentiable function at a point a e Zp and denote this property by f e UD Zp if the difference quotients Ff x y f x - f y x - y have a limit l f a as x y a a cf. 1-24 . For f e UD Zp the above distribution yq yields the bosonic p-adic invariant q-integral as follows Iq f f f x dfr x lirn E f WqX JZp N pN qx 0 1.4 .