In this paper, we prove sharp Hardy type integral inequality by using the generalized Riesz potential generated by the generalized Shift operator. Our results improve and extend the well-known results of Hardy.
Yin, L., Niu, D. W., & Qi, F. (2013). Some New Integral Inequalities. Tamkang Journal of Mathematics, 44(3), 279-288. https://doi.org/10.5556/j.tkjm.44.2013.1166