Hardy Inequalities on Homogeneous Groups

Michael Ruzhansky is a Professor of Pure Mathematics at Imperial College London.Durvudkhan Suragan is an Assistant Professor of Mathematics at Nazarbayev University.

“This book is devoted to Hardy inequalities and similar inequalities, Rellich, Sobolev, Caffarelli-Kohn-Nirenberg inequalities on homogeneous Lie groups. … The book is a well written exhaustive monograph of the subject. It contains also a rich bibliography.” (Leszek Skrzypczak, zbMATH 1428.22011, 2020)

• Introduction.- Analysis on Homogeneous Groups.- Hardy Inequalities on Homogeneous Groups.- Rellich, Caarelli-Kohn-Nirenberg, and Sobolev Type Inequalities.- Fractional Hardy Inequalities.- Integral Hardy Inequalities on Homogeneous Groups.- Horizontal Inequalities on Stratied Groups.- Hardy-Rellich Inequalities and Fundamental Solutions.- Geometric Hardy Inequalities on Stratied Groups.- Uncertainty Relations on Homogeneous Groups.- Function Spaces on Homogeneous Groups.- Elements of Potential Theory on Stratified Groups.- Hardy and Rellich Inequalities for Sums of Squares.- Bibliography.- Index.