Universal approximation of symmetrizations by polarizations

Schaftingen, Jean

doi:10.1090/S0002-9939-05-08325-5

Universal approximation of symmetrizations by polarizations
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by Jean van Schaftingen PDF

Proc. Amer. Math. Soc. 134 (2006), 177-186 Request permission

Abstract:

Any symmetrization (Schwarz, Steiner, cap or increasing rear- rangement) can be approximated by a universal sequence of polarizations which converges in $\mathrm {L}^p$ norm for any admissible function in $\mathrm {L}^p$ for $1 \le p < +\infty$ and uniformly for admissible continuous functions. A new Pólya-Szegö inequality is proved for the increasing rearrangement.

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