Stratified Lie Groups and Potential Theory for their Sub-Laplacians

Authors:

ISBN: 978-3-540-71896-3 (Print) 978-3-540-71897-0 (Online)

Table of contents (20 chapters)

  1. Front Matter

    Pages I-XXVI

  2. Elements of Analysis of Stratified Groups

    1. Front Matter

      Pages 1-1

    2. No Access

      Book Chapter

      Pages 3-85

      Stratified Groups and Sub-Laplacians

    3. No Access

      Book Chapter

      Pages 87-154

      Abstract Lie Groups and Carnot Groups

    4. No Access

      Book Chapter

      Pages 155-181

      Carnot Groups of Step Two

    5. No Access

      Book Chapter

      Pages 183-226

      Examples of Carnot Groups

    6. No Access

      Book Chapter

      Pages 227-333

      The Fundamental Solution for a Sub-Laplacian and Applications

  3. Elements of Potential Theory for Sub-Laplacians

    1. Front Matter

      Pages 335-335

    2. No Access

      Book Chapter

      Pages 337-380

      Abstract Harmonic Spaces

    3. No Access

      Book Chapter

      Pages 381-395

      The ℒ-harmonic Space

    4. No Access

      Book Chapter

      Pages 397-424

      ℒ-subharmonic Functions

    5. No Access

      Book Chapter

      Pages 425-472

      Representation Theorems

    6. No Access

      Book Chapter

      Pages 473-488

      Maximum Principle on Unbounded Domains

    7. No Access

      Book Chapter

      Pages 489-536

      ℒ-capacity, ℒ-polar Sets and Applications

    8. No Access

      Book Chapter

      Pages 537-555

      ℒ-thinness and ℒ-fine Topology

    9. No Access

      Book Chapter

      Pages 557-574

      d-Hausdorff Measure and ℒ-capacity

  4. Further Topics on Carnot Groups

    1. Front Matter

      Pages 575-575

    2. No Access

      Book Chapter

      Pages 577-591

      Some Remarks on Free Lie Algebras

    3. No Access

      Book Chapter

      Pages 593-619

      More on the Campbell–Hausdorff Formula

    4. No Access

      Book Chapter

      Pages 621-647

      Families of Diffeomorphic Sub-Laplacians

    5. No Access

      Book Chapter

      Pages 649-680

      Lifting of Carnot Groups

    6. No Access

      Book Chapter

      Pages 681-714

      Groups of Heisenberg Type

    7. No Access

      Book Chapter

      Pages 715-731

      The Carathéodory–Chow–Rashevsky Theorem

    8. No Access

      Book Chapter

      Pages 733-771

      Taylor Formula on Homogeneous Carnot Groups

  5. Back Matter

    Pages 773-803