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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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