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1988, A series of comprehensive studies in mathematics, ISBN 3540136150, Volume 285., xiv, 331
Book
1961, School ed., New mathematical library, Volume 4, 132
Book
2001, Cambridge tracts in mathematics, ISBN 0521802679, Volume 145., xii, 268
Book
Journal of Functional Analysis, ISSN 0022-1236, 08/2009, Volume 257, Issue 3, pp. 641 - 658
A new sharp affine L Sobolev inequality for functions on R is established. This inequality strengthens and implies the previously known affine L Sobolev... 
Sobolev inequalities | Affine isoperimetric inequalities
Journal Article
1951, Annals of mathematics studies, Volume no. 27., xvi, 279
Book
BERNOULLI, ISSN 1350-7265, 11/2019, Volume 25, Issue 4B, pp. 3978 - 4006
We investigate links between the so-called Stein's density approach in dimension one and some functional and concentration inequalities. We show that measures... 
weighted Poincare inequality | weighted log-Sobolev inequality | concentration inequality | tail bound | SIZE BIASED COUPLINGS | STATISTICS & PROBABILITY | SPECTRAL GAP | Stein kernel | isoperimetric constant | SOBOLEV INEQUALITIES | covariance identity
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 2009, Volume 257, Issue 3, pp. 641 - 658
A new sharp affine Sobolev inequality for functions on is established. This inequality strengthens and implies the previously known affine Sobolev inequality... 
Sobolev inequalities | Affine isoperimetric inequalities | MATHEMATICS | SHARP SOBOLEV | MINKOWSKI-FIREY THEORY | VALUATIONS | BODIES | ISOPERIMETRIC-INEQUALITIES
Journal Article
JOURNAL OF FUNCTIONAL ANALYSIS, ISSN 0022-1236, 07/2016, Volume 271, Issue 2, pp. 454 - 473
We show that the L-p Busemann-Petty centroid inequality provides an elementary and powerful tool to the study of some sharp affine functional inequalities with... 
MATHEMATICS | Affine Sobolev inequalities | L-p Busemann-Petty centroid inequality | HYPERCONTRACTIVITY | HAMILTON-JACOBI EQUATIONS | Affine logarithmic inequalities | ISOPERIMETRIC-INEQUALITIES
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 07/2015, Volume 427, Issue 2, pp. 905 - 929
Journal Article
1997, Memoirs of the American Mathematical Society, ISBN 0821806424, Volume no. 616., viii, 111
Book
Advances in Mathematics, ISSN 0001-8708, 11/2019, Volume 356, p. 106811
It is shown that every even, zonal measure on the Euclidean unit sphere gives rise to an isoperimetric inequality for sets of finite perimeter which directly... 
Sobolev inequality | Valuation | Isoperimetric inequality | MATHEMATICS | POLYA-SZEGO PRINCIPLE | PROJECTION BODIES | MINKOWSKI-FIREY THEORY | INVARIANT VALUATIONS | ENDOMORPHISMS | SOBOLEV
Journal Article
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 04/2019, Volume 372, Issue 4, pp. 2753 - 2776
We establish sharp affine weighted L^p Sobolev type inequalities by using the L_p Busemann-Petty centroid inequality proved by Lutwak, Yang, and Zhang. Our... 
MATHEMATICS | centroid bodies | Sobolev inequality | convex body | ISOPERIMETRIC-INEQUALITIES | MINKOWSKI
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 06/2017, Volume 56, Issue 3, p. 1
We provide a sharp quantitative version of the Gaussian concentration inequality: for every r > 0, the difference between the measure of the r-enlargement of a... 
60E15 | 49Q20 | 52A40 | MATHEMATICS | MATHEMATICS, APPLIED | STABILITY | Equality
Journal Article
Journal of Geometric Analysis, ISSN 1050-6926, 12/2018, Volume 28, Issue 4, pp. 3522 - 3552
Extremal functions are exhibited in Poincare trace inequalities for functions of bounded variation in the unit ball Bn of the n-dimensional Euclidean spaceRn.... 
Isoperimetric inequalities | Functions of bounded variation | Sobolev spaces | Boundary traces | Poincaré inequalities | Sharp constants | ISOPERIMETRIC INEQUALITY | CONSTANT | SOBOLEV INEQUALITIES | MATHEMATICS | BALLS | WORST | EXTREMAL-FUNCTIONS | Poincare inequalities
Journal Article
Geometriae Dedicata, ISSN 0046-5755, 04/2019, Volume 199, Issue 1, pp. 335 - 353
By proving a "weighted" reverse affine isoperimetric inequality and its dual, we establish a sharp L.sub.[infinity] L [infinity] Loomis--Whitney inequality and... 
Reverse affine isoperimetric inequality | Loomis–Whitney inequality | Isotropic measure | Weighted ℓ | balls | zonoid
Journal Article
Advances in Mathematics, ISSN 0001-8708, 02/2018, Volume 325, pp. 824 - 863
Given one metric measure space satisfying a linear Brunn–Minkowski inequality, and a second one satisfying a Brunn–Minkowski inequality with exponent , we... 
Gaussian measure | Isoperimetric inequality | Metric measure space | Product space | Product measure | Brunn–Minkowski inequality | MATHEMATICS | Brunn-Minkowski inequality
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2016, Volume 434, Issue 2, pp. 1676 - 1689
In this paper we prove that the disc is a maximiser of the Schatten -norm of the logarithmic potential operator among all domains of a given measure in , for... 
Pólya inequality | Characteristic numbers | Rayleigh–Faber–Krahn inequality | Isoperimetric inequality | Logarithmic potential | Schatten class | Rayleigh-Faber-Krahn inequality | LAPLACIAN | MATHEMATICS | EIGENVALUES | MATHEMATICS, APPLIED | Polya inequality | Mathematics - Functional Analysis
Journal Article
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