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.

• 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.

“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)