منابع مشابه
Lp AFFINE ISOPERIMETRIC INEQUALITIES
Affine isoperimetric inequalities compare functionals, associated with convex (or more general) bodies, whose ratios are invariant under GL(n)-transformations of the bodies. These isoperimetric inequalities are more powerful than their better-known relatives of a Euclidean flavor. To be a bit more specific, this article deals with inequalities for centroid and projection bodies. Centroid bodies...
متن کاملSHARP AFFINE Lp SOBOLEV INEQUALITIES
In this paper we prove a sharp affine Lp Sobolev inequality for functions on R. The new inequality is significantly stronger than (and directly implies) the classical sharp Lp Sobolev inequality of Aubin [A2] and Talenti [T], even though it uses only the vector space structure and standard Lebesgue measure on R. For the new inequality, no inner product, norm, or conformal structure is needed at...
متن کاملDUAL Lp AFFINE ISOPERIMETRIC INEQUALITIES
Corresponding to each convex (or more general) subset of n-dimensional Euclidean space, Rn, there is a unique ellipsoid with the following property. The moment of inertia of the ellipsoid and the moment of inertia of the convex set are the same about every 1-dimensional subspace of Rn. This ellipsoid is called the Legendre ellipsoid of the convex set. The Legendre ellipsoid is a well-known conc...
متن کاملInequalities on asymmetric Lp-harmonic radial bodies
Lutwak introduced the Lp-harmonic radial body of a star body. In this paper, we define the notion of asymmetric Lpharmonic radial bodies and study their properties. In particular, we obtain the extremum values of dual quermassintegrals and the volume of the polars of the asymmetric Lp-harmonic radial bodies, respectively. c ©2017 All rights reserved.
متن کاملLp inequalities for functionals of brownian motion
© Springer-Verlag, Berlin Heidelberg New York, 1987, tous droits réservés. L’accès aux archives du séminaire de probabilités (Strasbourg) (http://portail. mathdoc.fr/SemProba/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impressio...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1969
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1969-12403-1