Collecting all the results on the particular types of inequalities, the coverage of this book is unique among textbooks in the literature. The book focuses on the historical development of the Carlson inequalities and their many generalizations and variations. As well as almost all known results concerning these inequalities and all known proof techniques, a number of open questions suitable for further research are considered. Two chapters are devoted to clarifying the close connection between interpolation theory and this type of inequality. Other applications are also included, in addition to a historical note on Fritz Carlson himself.
Carlson's Inequalities; Some Extensions and Complements to Carlson's Inequalities; The Continuous Case; Levin's Theorem; Some Multi-Dimensional Generalizations and Variations; Some Carlson Type Inequalities for Weighted Lebesgue Spaces with General Measures; Carlson Type Inequalities and Real Interpolation Theory; Further Connection to Interpolation Theory, the Peetre Method; Related Results and Applications; Appendices: A Historical Note on Fritz David Carlson (1888-1952); A Translation of the Original Article by Carlson from French to English.