Equivalent Inequalities of the HÖlder Inequality for Integrable Functions

Abstract

HÖlder inequality plays an extremely important role in analysis and elementary in- equality theory. As an important aspect of related research, the study of its equiva-lence relationship with other inequalities has also received increasing attention. This paper proves the H¨older inequality and the AM-GM inequality in measure space, and its equivalence relationship with the power mean inequality. These results generalize the discrete inequality equivalence relationship recently established by Li etal.