On necessary and sufficient conditions for $L^p$-estimates of Riesz transforms associated to elliptic operators on $\RR^n$ and related estimates

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dc.creatorAuscher, Pascal
dc.date2005-06-02
dc.date2005-06-06
dc.date.accessioned2026-07-07T05:20:27Z
dc.date.available2026-07-07T05:20:27Z
dc.descriptionThis article 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. We introduce 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. We thus recover in a unified and coherent way many $L^p$ estimates and give 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 $(2,\infty)$.
dc.descriptionTo appear in Memoirs of the American Mathematical Society. A mistake corrected
dc.identifierhttps://arxiv.org/abs/math/0506032
dc.identifierhttp://arxiv.org/abs/math/0506032
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75387
dc.subjectClassical Analysis and ODEs
dc.subjectAnalysis of PDEs
dc.subjectFunctional Analysis
dc.subjectMSC 2000 numbers: 42B20, 42B25, 47F05, 47B44, 35J15, 35J30, 35J45
dc.titleOn necessary and sufficient conditions for $L^p$-estimates of Riesz transforms associated to elliptic operators on $\RR^n$ and related estimates
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