This paper deals with some new generalizations of Hardy's integral inequalities. Some cases concerning whether the constant factors involved in these inequalities are best possible are discussed in some detail.
Hussain, S., Latif, M. A., & Akhtar, W. (2012). Weighted Hardy Type Integral Inequalities Involving Many Functions. Tamkang Journal of Mathematics, 43(2), 301-311. https://www.airitilibrary.com/Article/Detail?DocID=00492930-201206-201206200011-201206200011-301-311