S. Iqbal, K. Krulic Himmelreich and J. Pecaric Received: March 29, 2013; Revised: January 24, 2014; Accepted: January 31, 2014 Abstract. The main purpose of this paper is to give the well-known Hardy, Pólya-Knopp, Hardy-Hilbert, Hardy-Littlewood-Pólya and Hilbert-Hardy-type inequalities in quotients. We apply our result on multidimensional setting to obtain new results. Keywords: Convex function; kernel; weights; Hardy's inequality; Pólya-Knopp's inequality; Hardy-Hilbert inequality; Hardy-Littlewood-Pólya inequality. AMS Subject classification: Primary: 26D15 Version to read: PDF ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2014, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |