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Fefferman’s original proof of Open image in new window

  • Akihito Uchiyama
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

$$ \left| {\smallint _{{\text{R}}^n } \vec Rf\left( {x.} \right) \cdot \vec g\left( x \right)dx} \right| \leqslant C\left( n \right)\left\| {\vec Rf} \right\|_{L^1 } \left\| {\vec g} \right\|_{{\text{BMO}}} $$
(19.1)
where
$$ f \in L^2 \left( {{\text{R}}^n ,{\text{R}}} \right),\vec g \in L^2 \left( {{\text{R}}^n ,{\text{R}}^{n + 1} } \right) $$
(19.2)
In Sections 19‐20, we let
$$ \begin{gathered} \Delta = D_t^2 + D_{x_1 }^2 + \cdots + D_{x_n }^2 ,\nabla = \nabla _{t,x} = \left( {D_t ,D_{x_1 } \cdots ,D_{x_n } } \right) \hfill \\ \left| {\nabla _u } \right| = \left\{ {\sum\limits_{j = 0}^n {\left( {D_{x_j } u} \right)^2 } } \right\}^{1/2} , \hfill \\ \left| {\nabla ^2 u} \right| = \left\{ {\sum\limits_{j = 0}^n {\sum\limits_{i = 0}^n {\left( {D_{x_j } D_{x_i } u} \right)^2 } } } \right\}^{1/2} ,{\text{where }}D_{x_0 } = D_t . \hfill \\ \end{gathered} $$

Keywords

Euclidean Space Harmonic Function Number Theory Algebraic Geometry Hardy Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Japan 2001

Authors and Affiliations

  • Akihito Uchiyama

There are no affiliations available

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