On Necessary and Sufficient Conditions for $L^p$-Estimates of Riesz Transforms Associated to Elliptic Operators on $\mathbb{R}^n$ and Related Estimates

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On Necessary and Sufficient Conditions for $L^p$-Estimates of Riesz Transforms Associated to Elliptic Operators on $\mathbb{R}^n$ and Related Estimates

Pascal Auscher : Université Paris-Sud, Orsay, France

On Necessary and Sufficient Conditions for L^p-Estimates of Riesz Transforms Associated to Elliptic Operators on R^n and Related Estimates

eBook ISBN:	978-1-4704-0475-8
Product Code:	MEMO/186/871.E

List Price:	$66.00
MAA Member Price:	$59.40
AMS Member Price:	$39.60

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On Necessary and Sufficient Conditions for $L^p$-Estimates of Riesz Transforms Associated to Elliptic Operators on $\mathbb{R}^n$ and Related Estimates

Pascal Auscher : Université Paris-Sud, Orsay, France

eBook ISBN:	978-1-4704-0475-8
Product Code:	MEMO/186/871.E

List Price:	$66.00
MAA Member Price:	$59.40
AMS Member Price:	$39.60

Add to cart

Book Details

Memoirs of the American Mathematical Society

Volume: 186; 2007; 75 pp

MSC: Primary 42; 47; 35

This memoir focuses on $L^p$ estimates for objects associated to elliptic operators in divergence form: its semigroup, the gradient of the semigroup, functional calculus, square functions and Riesz transforms. The author introduces four critical numbers associated to the semigroup and its gradient that completely rule the ranges of exponents for the $L^p$ estimates. It appears that the case $p<2$ already treated earlier is radically different from the case $p>2$ which is new. The author thus recovers in a unified and coherent way many $L^p$ estimates and gives further applications. The key tools from harmonic analysis are two criteria for $L^p$ boundedness, one for $p<2$ and the other for $p>2$ but in ranges different from the usual intervals $(1,2)$ and $(2,\infty)$.
Table of Contents
- Chapters
- 1. Beyond Calderón-Zygmund operators
- 2. Basic $L^2$ theory for elliptic operators
- 3. $L^p$ theory for the semigroup
- 4. $L^p$ theory for square roots
- 5. Riesz transforms and functional calculi
- 6. Square function estimates
- 7. Miscellani
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Book Details
Table of Contents
Requests

Memoirs of the American Mathematical Society

Volume: 186; 2007; 75 pp

MSC: Primary 42; 47; 35

This memoir focuses on $L^p$ estimates for objects associated to elliptic operators in divergence form: its semigroup, the gradient of the semigroup, functional calculus, square functions and Riesz transforms. The author introduces four critical numbers associated to the semigroup and its gradient that completely rule the ranges of exponents for the $L^p$ estimates. It appears that the case $p<2$ already treated earlier is radically different from the case $p>2$ which is new. The author thus recovers in a unified and coherent way many $L^p$ estimates and gives further applications. The key tools from harmonic analysis are two criteria for $L^p$ boundedness, one for $p<2$ and the other for $p>2$ but in ranges different from the usual intervals $(1,2)$ and $(2,\infty)$.

Chapters
1. Beyond Calderón-Zygmund operators
2. Basic $L^2$ theory for elliptic operators
3. $L^p$ theory for the semigroup
4. $L^p$ theory for square roots
5. Riesz transforms and functional calculi
6. Square function estimates
7. Miscellani

Review Copy – for publishers of book reviews

Permission – for use of book, eBook, or Journal content

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