A constructive proof of the Fefferman-Stein decomposition of BMO (Rn)

Abstract

Let $$ S_{\vec R} \left\{ {\left( {f, - R_1 f, \cdots , - R_n f} \right):f \in H^1 \left( {{\text{R}}^n ,{\text{R}}} \right)} \right\} \subset H^1 \left( {{\text{R}}^n ,{\text{R}}^{n + 1} } \right) $$ (22.1) $$ \begin{gathered} S_{\vec R} \left\{ {\vec g = \left( {g_j } \right)_{j = 0, \cdots ,n} } \right. \in {\text{BMO}}\left( {{\text{R}}^n ,{\text{R}}^{n + 1} } \right): \sum\limits_{j = 0}^n {\vec R_j } g_j = 0{\text{ in BMO}}\left( {{\text{R}}^n ,{\text{R}}^{n + 1} } \right)\left. {/{\text{R}}} \right\} \end{gathered} $$ (22.2) . j=0

Locations

• Acta Mathematica - View - PDF