Search results for "Log sum inequality"
showing 4 items of 4 documents
On factor decomposition of cross-country income inequality: some extensions and qualifications
2001
Abstract In a recent paper in this journal Duro and Esteban [Econom. Lett. 60 (1998) 269] have proposed a factor decomposition of the Theil [Economics and Information Theory, Amsterdam, North-Holland, 1967] index of inequality over per capita incomes into the (unweighted) sum of the inequality indexes of the factors in order to measure the contribution of each individual factor to the overall inequality. The purpose of this little note is to extend and qualify the meaning of such a decomposition, to show that the decomposition also holds for another Theil [Economics and Information Theory, Amsterdam, North-Holland, 1967], index of inequality and that both decompositions offer qualitatively …
Isoperimetric inequality from the poisson equation via curvature
2012
In this paper, we establish an isoperimetric inequality in a metric measure space via the Poisson equation. Let (X,d,μ) be a complete, pathwise connected metric space with locally Ahlfors Q-regular measure, where Q > 1, that supports a local L2-Poincare inequality. We show that, for the Poisson equation Δu = g, if the local L∞-norm of the gradient Du can be bounded by the Lorentz norm LQ,1 of g, then we obtain an isoperimetric inequality and a Sobolev inequality in (X,d,μ) with optimal exponents. By assuming a suitable curvature lower bound, we establish such optimal bounds on . © 2011 Wiley Periodicals, Inc.
Hardy’s inequality and the boundary size
2002
We establish a self-improving property of the Hardy inequality and an estimate on the size of the boundary of a domain supporting a Hardy inequality.
On improved fractional Sobolev–Poincaré inequalities
2016
We study a certain improved fractional Sobolev–Poincaré inequality on domains, which can be considered as a fractional counterpart of the classical Sobolev–Poincaré inequality. We prove the equivalence of the corresponding weak and strong type inequalities; this leads to a simple proof of a strong type inequality on John domains. We also give necessary conditions for the validity of an improved fractional Sobolev–Poincaré inequality, in particular, we show that a domain of finite measure, satisfying this inequality and a ‘separation property’, is a John domain.