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An asymmetric affine Pólya–Szegö principle

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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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Authors and Affiliations

  1. Department of Mathematics, University of Salzburg, Hellbrunner Straße 34, 5020, Salzburg, Austria

    Christoph Haberl

  2. Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040, Vienna, Austria

    Franz E. Schuster

  3. Department of Mathematics and Statistics, Memorial University, St. John’s, NL, A1C 5S7, Canada

    Jie Xiao

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  1. Christoph Haberl
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  2. Franz E. Schuster
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  3. Jie Xiao
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Correspondence to Jie Xiao.

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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

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