Stratified Lie Groups and Potential Theory for Their Sub-Laplacians Book

Part I: Elements of Analysis of Stratified Groups; Stratified Groups and sub-Laplacians.- Abstract Lie Groups and Carnot Groups.- Carnot Groups of Step Two.- Examples of Carnot Groups.- The Fundamental Solution for a sub-Laplacian and Applications.- Part II: Elements of Potential Theory for sub-Laplacians; Abstract Harmonic Spaces.- The L-harmonic Space.- L-subharmonic Functions.- Representation Theorems.- Maximum Principle on Unbounded Domains.- L-capacity, L-polar Sets and Applications.- L-thinness and L-fine Topology.- d-Hausdorff Measure and L-capacity.- Part III: Further Topics on Carnot Groups; Some Remarks on Free Lie Algebras.- More on the Campbell-Hausdorff Formula.- Families of Diffeomorphic sub-Laplacians.- Lifting of Carnot Groups.- Groups of Heisenberg Type.- The Carathéodory-Chow-Rashevsky Theorem.- Taylor Formula on Carnot Groups.