© Hindawi Publishing Corp. GENERALIZATIONS OF HÖLDER’S INEQUALITY

Abstract. Some generalized Hölder’s inequalities for positive as well as negative expo-nents are obtained. 2000 Mathematics Subject Classification. 26D07, 26D15. 1. Introduction. While the renowned inequality of Hölder [1] is well celebrated for its beauty and its wide range of important applications to real and complex analysis, functional analysis, as well asmany disciplines in appliedmathematics, it is a little less well known that it has a counterpart for negative exponents. Furthermore, it appears that nowhere in the literature contains a generalization of them to the case involvin