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On Necessary and Sufficient Conditions for Lp-estimates of Riesz Transforms Associated to Elliptic Operators on Rn and Related Estimates by Pascal Auscher
  

On Necessary and Sufficient Conditions for Lp-estimates of Riesz Transforms Associated to Elliptic Operators on Rn and Related Estimates

Part of the Memoirs of the American Mathematical Society Series

Synopsis

On Necessary and Sufficient Conditions for Lp-estimates of Riesz Transforms Associated to Elliptic Operators on Rn and Related Estimates by Pascal Auscher

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 $p2$ 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 $p2$ but in ranges different from the usual intervals $(1,2)$ and $(2,\infty)$.

About the Author

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Book Info

Publication date

15th February 2007

Author

Pascal Auscher

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Publisher

American Mathematical Society

Format

Paperback
75 pages

Categories

Functional analysis & transforms
Differential calculus & equations

ISBN

9780821839416

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