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Multi-parameter Singular Integrals I: Examples

Brian Street

in Multi-parameter Singular Integrals. (AM-189)

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691162515
eISBN:
9781400852758
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691162515.003.0004
Subject:
Mathematics, Analysis

This chapter discusses a few special cases where a theory of multi-parameter singular integral operators has already been developed. These include the product theory of singular integrals, ... More


Multi-parameter Singular Integrals. (AM-189)

Brian Street

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691162515
eISBN:
9781400852758
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691162515.001.0001
Subject:
Mathematics, Analysis

This book develops a new theory of multi-parameter singular integrals associated with Carnot–Carathéodory balls. The book first details the classical theory of Calderón–Zygmund singular integrals and ... More


Multi-parameter Singular Integrals II: General Theory

Brian Street

in Multi-parameter Singular Integrals. (AM-189)

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691162515
eISBN:
9781400852758
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691162515.003.0005
Subject:
Mathematics, Analysis

This chapter turns to a general theory which generalizes and unifies all of the examples in the preceding chapters. A main issue is that the first definition from the trichotomy does not generalize ... More


The Calder´on-Zygmund Theory II: Maximal Hypoellipticity

Brian Street

in Multi-parameter Singular Integrals. (AM-189)

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691162515
eISBN:
9781400852758
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691162515.003.0002
Subject:
Mathematics, Analysis

This chapter remains in the single-parameter case and turns to the case when the metric is a Carnot–Carathéodory (or sub-Riemannian) metric. It defines a class of singular integral operators adapted ... More


Analytic Elements from Singular Integral Equations

David R. Steward

in Analytic Element Method: Complex Interactions of Boundaries and Interfaces

Published in print:
2020
Published Online:
November 2020
ISBN:
9780198856788
eISBN:
9780191890031
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198856788.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Solutions to interface problems may be developed using analytic elements with mathematical solutions to the Laplace equation developed by singular integral equations. This formulation leads to ... More


Multi-parameter Carnot-Carath´eodory Geometry

Brian Street

in Multi-parameter Singular Integrals. (AM-189)

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691162515
eISBN:
9781400852758
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691162515.003.0003
Subject:
Mathematics, Analysis

This chapter develops the theory of multi-parameter Carnot–Carathéodory geometry, which is needed to study singular integral operators. In the case when the balls are of product type, all of the ... More


The Calder´on-Zygmund Theory I: Ellipticity

Brian Street

in Multi-parameter Singular Integrals. (AM-189)

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691162515
eISBN:
9781400852758
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691162515.003.0001
Subject:
Mathematics, Analysis

This chapter discusses a case for single-parameter singular integral operators, where ρ‎ is the usual distance on ℝn. There, we obtain the most classical theory of singular integrals, which is useful ... More


Analytic Element Method: Complex Interactions of Boundaries and Interfaces

David R. Steward

Published in print:
2020
Published Online:
November 2020
ISBN:
9780198856788
eISBN:
9780191890031
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198856788.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The Analytic Element Method provides a foundation to solve boundary value problems commonly encountered in engineering and science. The goals are: to introduce readers to the basic principles of the ... More


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