Affine Orlicz Pólya-Szegö principle for log-concave functions

The affine Lp Pólya-Szegö principle significantly strengthens the classical Pólya-Szegö principle. It is an open problem whether there exists an affine Orlicz Pólya-Szegö principle which includes the affine Lp Pólya-Szegö principle as special case. In this paper, an affine Orlicz Pólya-Szegö principle for log-concave functions is established by using functional Steiner symmetrizations.