On Necessary and Sufficient Conditions for Lp-estimates of Riesz Transforms Associated to Elliptic Operators on Rn and Related Estimates
Author:   Pascal Auscher
Publisher:   American Mathematical Society
Edition:   illustrated Edition
Volume:   No. 186
ISBN:  

9780821839416


Pages:   75
Publication Date:   01 March 2007
Format:   Paperback
Availability:   Temporarily unavailable   Availability explained
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On Necessary and Sufficient Conditions for Lp-estimates of Riesz Transforms Associated to Elliptic Operators on Rn and Related Estimates


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Overview

This memoir focuses on $Lp$ 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 $Lp$ 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 $Lp$ estimates and gives further applications. The key tools from harmonic analysis are two criteria for $Lp$ boundedness, one for $p<2$ and the other for $p>2$ but in ranges different from the usual intervals $(1,2)$ and $(2,\infty)$.

Full Product Details

Author:   Pascal Auscher
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
Edition:   illustrated Edition
Volume:   No. 186
Weight:   0.198kg
ISBN:  

9780821839416


ISBN 10:   0821839411
Pages:   75
Publication Date:   01 March 2007
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Temporarily unavailable   Availability explained
The supplier advises that this item is temporarily unavailable. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out to you.

Table of Contents

Beyond Calderon-Zygmund operators Basic $L^2$ theory for elliptic operators $L^p$ theory for the semigroup $L^p$ theory for square roots Riesz transforms and functional calculi Square function estimates Miscellani Appendix A. Calderon-Zygmund decomposition for Sobolev functions Appendix. Bibliography.

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