Elliott H. Lieb proved sharp forms of the Hardy–Littlewood–Sobolev inequality and related inequalities. The work determines optimal constants in bounds for singular integral expressions. Sharp constants distinguish an estimate that merely controls an integral from one that identifies its exact limiting strength, with consequences for analysis and mathematical physics.[ref]
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Elliott H. Lieb is an American mathematician and physicist recognized for his contributions to mathematical physics, particularly in the areas of statistical mechanics, quantum mechanics, and the theory of many-body systems. He has made significant advancements in understanding the mathematical foundations of thermodynamics and has worked on topics such as the Lieb-Thirring inequalities and the analysis of various physical models.