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Table of contents

  1. Front Matter
    Pages i-xvi
  2. Michael Ruzhansky, Durvudkhan Suragan
    Pages 1-10 Open Access
  3. Michael Ruzhansky, Durvudkhan Suragan
    Pages 11-70 Open Access
  4. Michael Ruzhansky, Durvudkhan Suragan
    Pages 71-127 Open Access
  5. Michael Ruzhansky, Durvudkhan Suragan
    Pages 129-189 Open Access
  6. Michael Ruzhansky, Durvudkhan Suragan
    Pages 191-235 Open Access
  7. Michael Ruzhansky, Durvudkhan Suragan
    Pages 237-269 Open Access
  8. Michael Ruzhansky, Durvudkhan Suragan
    Pages 271-329 Open Access
  9. Michael Ruzhansky, Durvudkhan Suragan
    Pages 331-372 Open Access
  10. Michael Ruzhansky, Durvudkhan Suragan
    Pages 373-388 Open Access
  11. Michael Ruzhansky, Durvudkhan Suragan
    Pages 389-403 Open Access
  12. Michael Ruzhansky, Durvudkhan Suragan
    Pages 405-450 Open Access
  13. Michael Ruzhansky, Durvudkhan Suragan
    Pages 451-500 Open Access
  14. Michael Ruzhansky, Durvudkhan Suragan
    Pages 501-543 Open Access
  15. Back Matter
    Pages 545-571

About this book

Introduction

This open access book provides an extensive treatment of Hardy inequalities and closely related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The place where Hardy inequalities and homogeneous groups meet is a beautiful area of mathematics with links to many other subjects. While describing the general theory of Hardy, Rellich, Caffarelli-Kohn-Nirenberg, Sobolev, and other inequalities in the setting of general homogeneous groups, the authors pay particular attention to the special class of stratified groups. In this environment, the theory of Hardy inequalities becomes intricately intertwined with the properties of sub-Laplacians and subelliptic partial differential equations. These topics constitute the core of this book and they are complemented by additional, closely related topics such as uncertainty principles, function spaces on homogeneous groups, the potential theory for stratified groups, and the potential theory for general Hörmander's sums of squares and their fundamental solutions.

This monograph is the winner of the 2018 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics. As can be attested as the winner of such an award, it is a vital contribution to literature of analysis not only because it presents a detailed account of the recent developments in the field, but also because the book is accessible to anyone with a basic level of understanding of analysis. Undergraduate and graduate students as well as researchers from any field of mathematical and physical sciences related to analysis involving functional inequalities or analysis of homogeneous groups will find the text beneficial to deepen their understanding.

Keywords

Rellich inequality stratified group anisotropic analysis potential theory functional inequalities on Lie groups Open Access

Authors and affiliations

  • Michael Ruzhansky
    • 1
  • Durvudkhan Suragan
    • 2
  1. 1.Department of MathematicsImperial College London, UK; Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium; School of Mathematical Sciences, Queen Mary University of LondonLondonUK
  2. 2.Department of MathematicsNazarbayev UniversityAstanaKazakhstan

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-02895-4
  • Copyright Information The Editor(s) (if applicable) and The Author(s) 2019
  • License CC BY
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-02894-7
  • Online ISBN 978-3-030-02895-4
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • Buy this book on publisher's site