Stratified Lie Groups and Potential Theory for Their Sub-Laplacians (eBook)

1) ERMANNO LANCONELLI: --Education and Undergraduate Studies: Dec. 1966, Universita' di Bologna (Mathematics). Career/Employment: 1975-present: Full Professor of Mathematical Analysis at Dipartimento di Matematica, Universita' di Bologna (Italy); Member of the "Accademia dell'Istituto di Bologna" and of the "Accademia delle Scienze, Lettere ed Arti di Modena". 1968-1975: Theaching Assistant at Istituto di Matematica, Universita' di Bologna. --Academic activity: Director of the Istituto di Matematica di Bologna(1978/80), Director of the Undergraduate Mathematics Program, University of Bologna (1990/1999, 2000-2002, 2006-present) Director of PHD program, University of Bologna (1986/91, 1997/2000) --INVITATIONS: -University of Minnesota, Minneapolis (USA) -University of Purdue, West La Fayette, Indiana (USA) -Temple University, Philadelphia, Pennsylvania (USA) -Rutgers University, New Brunswick, New Jersey (USA) -University of Bern, Switzerland -- Specialization main fields: Partial Differential Equations, Potential Theory --CURRENT RESEARCH INTEREST: Second order linear and nonlinear partial differential equations with non- negative characteristic form and application to complex geometry and diffusion processes. Potential Theory and Harmonic Analysis in sub-riemannian settings. Real analysis and geometric methods. --EDITORIAL BOARD: Nonlinear Differential Equations and Applications, Birkhauser. --PUBLICATIONS: More than 70 papers in refereed journals. 2) UGUZZONI FRANCESCO: --Education and Undergraduate Studies: Dec. 1994, Universita' di Bologna (Mathematics) Career/Employment: February 2000: Ph.D. in Mathematical Analysis at Dipartimento di Matematica, Universita' di Bologna (Italy). October 1998: Assistant Professor at Dipartimento di Matematica, Universita' di Bologna. --CURRENT RESEARCH INTEREST: Second order linear and nonlinear partial differential equations with non- negative characteristic form and applications. Harmonic Analysis in sub- riemannian settings. --PUBLICATIONS: About 30 papers in refereed journals. 3) ANDREA BONFIGLIOLI: --Education and Undergraduate Studies: July 1998, Universita' di Bologna (Mathematics) --Career/Employment: March 2002: Ph.D. in Mathematical Analysis at Dipartimento di Matematica, Universita' di Bologna (Italy). November 2006: Assistant Professor at Dipartimento di Matematica, Universita' di Bologna. --CURRENT RESEARCH INTEREST: Second order linear partial differential equations with non-negative characteristic form and applications. Potential Theory in stratified Lie groups. --PUBLICATIONS: About 20 papers in refereed journals.

Preface 6
Contents 19
Elements of Analysis of Stratified Groups 25
1 Stratified Groups and Sub-Laplacians 26
2 Abstract Lie Groups and Carnot Groups 109
3 Carnot Groups of Step Two 177
4 Examples of Carnot Groups 204
5 The Fundamental Solution for a Sub-Laplacian and Applications 248
Elements of Potential Theory for Sub- Laplacians 355
6 Abstract Harmonic Spaces 356
7 The L- harmonic Space 400
8 L- subharmonic Functions 415
9 Representation Theorems 443
10 Maximum Principle on Unbounded Domains 491
11 L- capacity, L- polar Sets and Applications 507
12 L- thinness and L- fine Topology 555
13 d- Hausdorff Measure and L- capacity 574
Further Topics on Carnot Groups 592
14 Some Remarks on Free Lie Algebras 593
15 More on the Campbell–Hausdorff Formula 608
16 Families of Diffeomorphic Sub-Laplacians 635
17 Lifting of Carnot Groups 662
18 Groups of Heisenberg Type 694
19 The Carathéodory–Chow–Rashevsky Theorem 728
20 Taylor Formula on Homogeneous Carnot Groups 745
References 784
Index of the Basic Notation 799
Index 805