Abstract
An affine rearrangement inequality is established which strengthens and implies the recently obtained affine Pólya–Szegö symmetrization principle for functions on \({\mathbb R^n}\) . Several applications of this new inequality are derived. In particular, a sharp affine logarithmic Sobolev inequality is established which is stronger than its classical Euclidean counterpart.
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Dedicated to Erwin Lutwak on the occasion of his sixty-fifth birthday.
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Haberl, C., Schuster, F.E. & Xiao, J. An asymmetric affine Pólya–Szegö principle. Math. Ann. 352, 517–542 (2012). https://doi.org/10.1007/s00208-011-0640-9
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DOI: https://doi.org/10.1007/s00208-011-0640-9