Multi-parameter singular integrals
This book develops a new theory of multi-parameter singular integrals associated with Carnot-Carathéodory balls. Brian Street first details the classical theory of Calderón-Zygmund singular integrals and applications to linear partial differential equations. He then outlines the theory of multi-parameter Carnot-Carathéodory geometry, where the main tool is a quantitative version of the classical theorem of Frobenius. Street then gives several examples of multi-parameter singular integrals arisi…
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- Full title :Multi-parameter singular integrals / Brian Street.
Summary
This book develops a new theory of multi-parameter singular integrals associated with Carnot-Carathéodory balls. Brian Street first details the classical theory of Calderón-Zygmund singular integrals and applications to linear partial differential equations. He then outlines the theory of multi-parameter Carnot-Carathéodory geometry, where the main tool is a quantitative version of the classical theorem of Frobenius. Street then gives several examples of multi-parameter singular integrals arising naturally in various problems. The final chapter of the book develops a general theory of singular integrals that generalizes and unifies these examples.
Read More ↓Edition Statements
- Publication Date:©2014
Publication Statements
- Publisher(s):Princeton University Press
- Place of Publication:Princeton
- Language:eng
- Publication Date:©2014
The Physical Object
- Description:1 online resource (xiii, 395 pages)
Edition Identifiers
- ISBN:9781400852758, 1400852757, 9781306823975, 1306823978
- DOI:10.1515/9781400852758
- oclc:ocn881286436
- LC Classification:QA329.6
- Dewey Decimal:515/.98
Table of Contents
Cover; Contents; Preface; 1 The Calderón-Zygmund Theory I: Ellipticity; 1.1 Non-homogeneous kernels; 1.2 Non-translation invariant operators; 1.3 Pseudodifferential operators; 1.4 Elliptic equations; 1.5 Further reading and references; 2 The Calderón-Zygmund Theory II: Maximal Hypoellipticity; 2.1 Vector fields with formal degrees; 2.2 The Frobenius theorem; 2.2.1 Scaling techniques; 2.2.2 Ideas in the proof; 2.3 Vector fields with formal degrees revisited; 2.4 Maximal hypoellipticity; 2.4.1 Subellipticity; 2.4.2 Scale invariance; 2.5 Smooth metrics and bump functions; 2.6 The sub-Laplacian.
2.7 The algebra of singular integrals2.7.1 More on the cancellation condition; 2.8 The topology; 2.9 The maximal function; 2.10 Non-isotropic Sobolev spaces; 2.11 Maximal hypoellipticity revisited; 2.11.1 The Kohn Laplacian; 2.12 Exponential maps; 2.13 Nilpotent Lie groups; 2.14 Pseudodifferential operators; 2.15 Beyond Hörmander's condition; 2.15.1 More on the assumptions; 2.15.2 When the vector fields span; 2.15.3 When the vector fields do not span; 2.15.4 A Littlewood-Paley theory; 2.15.5 The role of real analyticity; 2.16 Further reading and references.
3 Multi-parameter Carnot-Carathéod…
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