منابع مشابه
Some Matrix Rearrangement Inequalities
We investigate a rearrangement inequality for pairs of n × n matrices: Let ‖A‖p denote (Tr(A∗A)p/2)1/p, the C trace norm of an n×n matrix A. Consider the quantity ‖A+B‖p+‖A−B‖p. Under certain positivity conditions, we show that this is nonincreasing for a natural “rearrangement” of the matrices A and B when 1 ≤ p ≤ 2. We conjecture that this is true in general, without any restrictions on A and...
متن کاملRelative rearrangement and interpolation inequalities
We prove here that the Poincaré-Sobolev pointwise inequalities for the relative rearrangement can be considered as the root of a great number of inequalities in various sets not necessarily vector spaces. In particular, new interpolation inequalities can be derived. Reordenamiento relativo y desigualdades de interpolación Resumen. Mostramos que las desigualdades puntuales de Poincaré-Sobolev pa...
متن کاملA Short Course on Rearrangement Inequalities
These notes grew out of introductory courses for graduate students that I gave at the First IMDEA Winter School in Madrid in January 2009, and at the Università di Napoli “Federico II” in April 2009. The manuscript has been been slightly expanded to five sections, each providing material for one or two hours of lecture. The first section gives an overview of the classical rearrangement inequali...
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This paper is motivated by a large variety of convex or non convex problems arising in symmetric and asymmetric information models. An existence theorem is proven, based on a supermodular version of Hardy-Littlewood’s rearrangement inequalities. Sufficient conditions for monotonicity of optimal solutions are provided. Several applications to insurance are given.
متن کاملRearrangement inequalities for functionals with monotone integrands
Abstract The inequalities of Hardy-Littlewood and Riesz say that certain integrals involving products of two or three functions increase under symmetric decreasing rearrangement. It is known that these inequalities extend to integrands of the form F (u1, . . . , um) where F is supermodular; in particular, they hold when F has nonnegative mixed second derivatives ∂i∂jF for all i 6= j. This paper...
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ژورنال
عنوان ژورنال: Journal of Multivariate Analysis
سال: 1987
ISSN: 0047-259X
DOI: 10.1016/0047-259x(87)90156-4