A constructive proof of the Fefferman- Stein decomposition of BMO

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


$$ S_{\vec R} \left\{ {\left( {f, - R_1 f, \cdots , - R_n f} \right):f \in H^1 \left( {{\text{R}}^n ,{\text{R}}} \right)} \right\} \subset H^1 \left( {{\text{R}}^n ,{\text{R}}^{n + 1} } \right) $$
$$ \begin{gathered} S_{\vec R} \left\{ {\vec g = \left( {g_j } \right)_{j = 0, \cdots ,n} } \right. \in {\text{BMO}}\left( {{\text{R}}^n ,{\text{R}}^{n + 1} } \right): \\ \sum\limits_{j = 0}^n {\vec R_j } g_j = 0{\text{ in BMO}}\left( {{\text{R}}^n ,{\text{R}}^{n + 1} } \right)\left. {/{\text{R}}} \right\} \\ \end{gathered} $$
. j=0


Euclidean Space Number Theory Algebraic Geometry Hardy Space Point Mass 
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© Springer Japan 2001

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  • Akihito Uchiyama

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