Convolution inequalities in Lorentz spaces

In this paper we study boundedness of the convolution operator in different Lorentz spaces. In particular, we obtain the limit case of the Young-O'Neil inequality in the classical Lorentz spaces. We also investigate the convolution operator in the weighted Lorentz spaces. Finally, norm inequalities for the potential operator are presented.

Accounting for the dead in the longitudinal analysis of income-related health inequalities

This paper develops an accounting framework to consider the effect of deaths on the longitudinal analysis of income-related health inequalities. Ignoring deaths or using inverse probability weights (IPWs) to re-weight the sample for mortality-related attrition can produce misleading results, since to do so would be to disregard the most extreme of all health outcomes. Incorporating deaths into the longitudinal analysis of income-related health inequalities provides a more complete picture in terms of the evaluation of health changes in respect to socioeconomic status. We illustrate our work by investigating health mobility in Quality Adjusted Life Years (QALYs) as measured by the SF6D from 1999 till 2004 using the British Household Panel Survey (BHPS). We show that for Scottish males explicitly accounting for the dead, rather than using IPWs to account for mortality-related attrition, changes the direction of the relationship between relative health changes and initial income position, while for other population groups it increases the strength of this relationship by up to 14 times. When deaths are explicitly incorporated into the analysis it is found that over this five year period for both Scotland and England & Wales the relative health changes were significantly regressive such that the poor experienced a larger share of the health losses relative to their initial share of health and a large amount of this was related to mortality.

Development of tools to measure and explain changes in health inequalities in Scotland and benchmark performance

This project will develop a modelling framework to explain changes in income-related health inequalities and benchmark the performance of Scotland in tackling income-related health inequalities, both over time and relative to that of England and Wales.

Inequalities in Child Mortality in India: A District-Level Analysis

This paper measures the degree of inequality in child mortality rates across districts in India, using data from the 1981, 1991 and 2001 Indian population censuses. The results show that child mortality is more concentrated in less developed districts in all three census years. Further, between 1981 and 2001, the inequality in child mortality seems to have increased to the advantage of the more developed districts (i.e., there was an increasing concentration of child mortality in less developed districts). However, the inequality in female child mortality rates seems to have declined between 1991 and 2001, even as it increased – albeit at a slower rate than before – for male child mortality rates. In the decomposition analysis, it is found that while a more equitable distribution of medical facilities and safe drinking water across districts did contribute towards reducing inequality in child mortality between 1981 and 1991, different levels of structural change among districts were responsible for a very large part of the inequality in child mortality to the advantage of the more developed districts in all three census years. Other variables which played important roles in increasing inequality included a measure of infrastructure development, female literacy, and a social group status variable. The paper concludes with some brief comments on the policy implications of the findings.

My Group Beats Your Group: Evaluating Non-Income Inequalities

This paper proposes a new methodology, the Domination Index, to evaluate non-income inequalities between social groups such as inequalities of educational attainment, occupational status, health or subjective well-being. The Domination Index does not require specific cardinalisation assumptions, but only uses the ordinal structure of these non-income variables. We approach from an axiomatic perspective and show that a set of desirable properties for a group inequality measure when the variable of interest is ordinal, characterizes the Domination Index up to a positive scalar transformation. Moreover we make use of the Domination Index to explore the relation between inequality and segregation and show how these two concepts are related theoretically.

Norm convolution inequalities in Lebesgue spaces

We obtain upper and lower estimates of the (p; q) norm of the con-volution operator. The upper estimate sharpens the Young-type inequalities due to O'Neil and Stepanov.

A characterization of two weight norm inequalities for maximal singular integrals

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Two weight inequalities for discrete positive operators

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Two weight inequalities for maximal truncations of dyadic Calderón-Zygmund operators

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Weighted norm inequalities for Fourier transforms of radial functions

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What are the causes of educational inequalities and of their evolution over time in Europe? Evidence from PISA

This paper provides evidence on the sources of differences in inequalities in educational scores in European Union member states, by decomposing them into their determining factors. Using PISA data from the 2000 and 2006 waves, the paper shows that inequalities emerge in all countries and in both period, but decreased in Germany, whilst they increased in France and Italy. Decomposition shows that educational inequalities do not only reflect background related inequality, but especially schools’ characteristics. The findings allow policy makers to target areas that may make a contribution in reducing educational inequalities.

Refined asymptotics for the subcritical Keller-Segel system and related functional inequalities

We analyze the rate of convergence towards self-similarity for the subcritical Keller-Segel system in the radially symmetric two-dimensional case and in the corresponding one-dimensional case for logarithmic interaction. We measure convergence in Wasserstein distance. The rate of convergence towards self-similarity does not degenerate as we approach the critical case. As a byproduct, we obtain a proof of the logarithmic Hardy-Littlewood-Sobolev inequality in the one dimensional and radially symmetric two dimensional case based on optimal transport arguments. In addition we prove that the onedimensional equation is a contraction with respect to Fourier distance in the subcritical case.

On stability of solutions to systems of convex inequalities

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