Gen. Math. Notes, Vol. 20, No. 1, January 2014, pp. 58-66 ISSN 2219-7184; Copyright © ICSRS Publication, 2014 www.i-csrs.org Available free online at http://www.geman.in On Some Integral Inequalities Analogs to Hilbert's Inequality Atta A.K. Abu Hany Department of Mathematics Alazhar University of Gaza, Gaza E-mail: attahany@gmail.com (Received: 18-10-13 / Accepted: 24-11-13) Abstract In this paper we give some further extensions of well-known Hilbert's inequality. We give equivalent form in two dimensions as application. Keywords: Hilbert's inequality, Hardy-Hilbert’s Inequality, equivalent form. 1 Introduction The well-known Hilbert's inequality and its equivalent form are presented first: Theorem A: [4] If f and g   , then the following inequalities hold and are equivalent                                  (1) and                      , (2)