Monatshefte für Mathematik

, Volume 179, Issue 1, pp 113–127 | Cite as

Asymmetric \(L_{p}\) convexification and the convex Lorentz–Sobolev inequality



An asymmetric version of the concept of \(L_{p}\) convexification of level sets is obtained for piecewise affine functions. Applications to the anisotropic convex Lorentz–Sobolev inequality and the anisotropic Pólya–Szegö principle are discussed.


Asymmetric \(L_{p}\) convexification Asymmetric convex Lorentz–Sobolev inequality Asymmetric Pólya–Szegö principle 

Mathematics Subject Classification

52A40 52A39 



The author wants to thank Monika Ludwig from the Vienna University of Technology for her valuable advice and both referees for their improvement suggestions leading to this version of the article.


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© Springer-Verlag Wien 2015

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of SalzburgSalzburgAustria

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