Shadow systems of asymmetric<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:math>zonotopes

Weberndorfer, Manuel

doi:10.1016/j.aim.2013.02.022

Cited by 38 publications

(19 citation statements)

References 40 publications

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“…This classification of extremal functions seems to be new. For other asymmetric functional inequalities, see, e.g., [48,50,57,63].…”

Section: Applications To Affine Sobolev-type Inequalitiesmentioning

confidence: 99%

New approach to the affine Pólya–Szegö principle and the stability version of the affine Sobolev inequality

Nguyen

2016

Advances in Mathematics

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Inspired by a recent work of Haddad, Jiménez and Montenegro, we give a new and simple approach to the recently established general affine Pólya-Szegö principle. Our approach is based on the general L p Busemann-Petty centroid inequality and does not rely on the general L p Petty projection inequality or the solution of the L p Minkowski problem. A Brothers-Ziemer-type result for the general affine Pólya-Szegö principle is also established. As applications, we reprove some sharp affine Sobolev-type inequalities and settle their equality conditions. We also prove a stability estimate for the affine Sobolev inequality on functions of bounded variation by using our new approach. As a corollary of this stability result, we deduce a stability estimate for the affine logarithmic-Sobolev inequality.

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“…This classification of extremal functions seems to be new. For other asymmetric functional inequalities, see, e.g., [48,50,57,63].…”

Section: Applications To Affine Sobolev-type Inequalitiesmentioning

confidence: 99%

New approach to the affine Pólya–Szegö principle and the stability version of the affine Sobolev inequality

Nguyen

2016

Advances in Mathematics

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“…, v m } and let μ({v i }) = c i > 0. Then condition (39) is satisfied since the measure μ is a discrete complex isotropic measure on S 2n−1 . By (8) and (35), we have for x ∈ R 2n ,…”

Section: Corollary 63 Suppose P ∈ [1 ∞] and μ Is A Complex Cross Mementioning

confidence: 99%

Volume inequalities for complex isotropic measures

Huang

2014

Geom Dedicata

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“…In 2017, Li and Wang [5] researched asymmetric L p -harmonic radial bodies by introducing parameter τ, their work belongs to the new and rapidly evolving asymmetric L p -Brunn-Minkowski theory. In fact, as an important content in convex geometry, this theory has its origins in the works of Ludwig, Haberl and Schuster [6][7][8][9][10][11], and was further developed in many articles (see [12][13][14][15][16][17][18][19][20][21]).…”

Section: Introductionmentioning

confidence: 99%

Asymmetric Orlicz Radial Bodies

Wang

2019

Mathematics

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Based on the L p -harmonic radial combination, Li and Wang researched the asymmetric L p -harmonic radial bodies, which belong to the asymmetric L p -Brunn-Minkowski theory initiated by Ludwig, Haberl and Schuster. In this paper, combined with Orlicz radial combination, we introduce the asymmetric Orlicz radial bodies and research their properties. Further, we also establish some inequalities for this concept.

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Shadow systems of asymmetricLpzonotopes

Cited by 38 publications

References 40 publications

New approach to the affine Pólya–Szegö principle and the stability version of the affine Sobolev inequality

New approach to the affine Pólya–Szegö principle and the stability version of the affine Sobolev inequality

Volume inequalities for complex isotropic measures

Asymmetric Orlicz Radial Bodies

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