On Necessary and Sufficient Conditions for LP-Estimates of Riesz Transforms Associated to Elliptic Operators on RN and Related Estimates

Released on by Pascal Auscher
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  • On Necessary and Sufficient Conditions for LP-Estimates of Riesz Transforms Associated to Elliptic Operators on RN and Related Estimates Book Detail

  • Author : Pascal Auscher
  • Release Date : 2014-09-11
  • Publisher : American Mathematical Society(RI)
  • Genre : MATHEMATICS
  • Pages : 102
  • ISBN 13 : 9781470404758
  • File Size : 73,73 MB
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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 PDF Summary

Book Description: 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 $(2, \infty)$.

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