Rearrangement methods in the work of Elliott Lieb
Rupert L. FrankCalifornia Institute of Technology, Pasadena, United States of America; Ludwig-Maximilians-Universität München, Germany; and Caltech, Pasadena, USA
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We review some topics in the theory of symmetric decreasing rearrangements with a particular focus on Lieb’s fundamental contributions. Topics covered include the Brascamp–Lieb–Luttinger theorem, the sharp Young and Hardy–Littlewood–Sobolev inequalities, as well as the continuity of the rearrangement map on Sobolev spaces.