The Pólya-Szegö Principle and the Anisotropic Convex Lorentz-Sobolev Inequality
نویسندگان
چکیده
An anisotropic convex Lorentz-Sobolev inequality is established, which extends Ludwig, Xiao, and Zhang's result to any norm from Euclidean norm, and the geometric analogue of this inequality is given. In addition, it implies that the (anisotropic) Pólya-Szegö principle is shown.
منابع مشابه
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An affine rearrangement inequality is established which strengthens and implies the recently obtained affine Pólya–Szegö symmetrization principle for functions on R. 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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ورودعنوان ژورنال:
دوره 2014 شماره
صفحات -
تاریخ انتشار 2014