Sharp inequalities for functional integrals and traces of conformally invariant operators

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Fractional conformal Laplacians and fractional Yamabe problems (2010, methodology): “Such inequality for the sphere case was also considered independently by Beckner [4], Branson [5], and Morpurgo [35], in the setting of interwining operators.”
Remainder terms in the fractional Sobolev inequality (2012, methodology): “This formula is most easily derived by considering the inverse of As and using the Funk-Hecke formula, see [4] and also [23].”
Compactness via symmetrization (2004, background): “Let be a sequence of nonnegative functions on that vanish at infinity, and let be a symmetrically decreasing function.”
Rearrangement inequalities for functionals with monotone integrands (2005, background): “Equality cases have also been determined in these situations [27, 5, 25, 26].”