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The Resource Multi-parameter singular integrals, Brian Street

Multi-parameter singular integrals, Brian Street

Label
Multi-parameter singular integrals
Title
Multi-parameter singular integrals
Statement of responsibility
Brian Street
Creator
Author
Subject
Language
eng
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
Member of
Cataloging source
N$T
Index
index present
Language note
In English
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
Annals of mathematics studies
Series volume
number 189
Multi-parameter singular integrals, Brian Street
Label
Multi-parameter singular integrals, Brian Street
Link
http://www.jstor.org/stable/10.2307/j.ctt6wq1bt
Publication
Copyright
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Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
mixed
Content category
text
Content type code
txt
Content type MARC source
rdacontent
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-Carathéodory Geometry3.1 Assumptions on the vector fields; 3.2 Some preliminary estimates; 3.3 The maximal function; 3.4 A Littlewood-Paley theory; 3.5 Further reading and references; 4 Multi-parameter Singular Integrals I: Examples; 4.1 The product theory of singular integrals; 4.1.1 Non-isotropic Sobolev spaces; 4.1.2 Further reading and references; 4.2 Flag kernels on graded groups and beyond; 4.2.1 Non-isotropic Sobolev spaces; 4.2.2 Further reading and references; 4.3 Left and right invariant operators; 4.3.1 An example of Kohn
  • 4.3.2 Further reading and references4.4 Carnot-Carathéodory and Euclidean geometries; 4.4.1 The [omitted]-Neumann problem; 4.4.2 Further reading and references; 5 Multi-parameter Singular Integrals II: General Theory; 5.1 The main results; 5.1.1 Non-isotropic Sobolev spaces; 5.1.2 Multi-parameter pseudodifferential operators; 5.1.3 Adding parameters; 5.1.4 Pseudolocality; 5.2 Schwartz space and product kernels; 5.3 Pseudodifferential operators and A[sub(3)] 6"A[sub(4)]; 5.4 Elementary operators and A[sub(4)] 6"A[sub(3)]; 5.5 A[sub(4)] 6"A[sub(2)] 6"A[sub(1)]; 5.6 A[sub(1)] 6"A[sub(4)]
  • 5.7 The topology5.8 Non-isotropic Sobolev spaces; 5.9 Adding parameters; 5.10 Pseudolocality; 5.10.1 Operators on a compact manifold; 5.11 Examples; 5.11.1 Euclidean vector fields; 5.11.2 Hörmander vector fields and other geometries; 5.11.3 Carnot-Carathéodory and Euclidean geometries; 5.11.4 An Example of Kohn; 5.11.5 The product theory of singular integrals; 5.12 Some generalizations; 5.13 Closing remarks; A Functional Analysis; A.1 Locally convex topological vector spaces; A.1.1 Duals and distributions; A.2 Tensor Products; B Three Results from Calculus; B.1 Exponential of vector fields
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Dimensions
unknown
http://library.link/vocab/discovery_link
{'f': 'http://opac.lib.rpi.edu/record=b4331675'}
Extent
1 online resource (xiii, 395 pages).
Form of item
online
Isbn
9781400852758
Media category
computer
Media MARC source
rdamedia
Media type code
c
Specific material designation
remote

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