What evidence is there to demonstrate growing inequality within nations but also growing equality between nations?

Jos Verbeek in his article titled “Increasingly, inequality within, not across, countries is rising” attempts to answer the question posed herein by listing various articles that can be used as sources of evidence. He cites evidence from a presentation given by Hans Rosling that states that “for the 21st century, a binary distinction of countries on the basis of their wealth is outdated." This is because the boundaries between the rich and the poor countries are less distinct owing to the great economic strides achieved by a majority of countries.
To support the notion that in-country inequalities, on the other hand, have increased, Verbeek cites information given by Atkinson et al (2011) that explains the “concentration of wealth on the top tail of the income distribution” especially in the United States, India, and China. Atkinson et al (2011) look at the changes in the top 1% of income for 22 countries over a given period of time. They suggest that since the 1980s, the richest 1% of the population account for a growing part of the national income in many countries.
Outside of sources listed in Verbeek’s article, another source of evidence is Vieira (2012), who states that national inequalities are increasing in all countries, with the exception of a few countries in Latin America. Vieira (2012) further highlights some drivers of recent rising inequalities such as globalization, increased production due to high technology use and “regulatory reforms within the labor market." Further, facts and figures given by the United Nations suggest that on average, income inequality in developing countries rose by 11% between 1990 and 2010. Qureshi, in his article titled “Trends in Income Inequality: Global, Inter-Country, and Within Countries," states that “over the last three decades, inequality between countries has decreased, while inequality within countries has increased." To support the decrease in inter-country inequality, Qureshi cites economic reforms and growth in big Asian countries such as China and India. He further asserts that this decrease was particularly felt after the year 2000.
https://blogs.worldbank.org/developmenttalk/increasingly-inequality-within-not-across-countries-rising

https://www.un.org/en/development/desa/policy/wess/wess_bg_papers/bp_wess2013_svieira1.pdf