|
|
| |
| DECOMPOSITION OF BMO FUNCTIONS AND FACTORIZATION OF $\[{A_p}\]$ WEIGHTS IN MARTINGALE SETTING |
| |
Citation： |
Long Ruilin,Peng Lizhong.DECOMPOSITION OF BMO FUNCTIONS AND FACTORIZATION OF $\[{A_p}\]$ WEIGHTS IN MARTINGALE SETTING[J].Chinese Annals of Mathematics B,1983,4(1):117~128 |
| Page view： 778
Net amount： 710 |
Authors： |
Long Ruilin; Peng Lizhong |
|
|
| Abstract： |
Let $\[(\Omega ,F,\mu )\]$ be a probabilty space with an increasing family $\[{\{ {F_t}\} _{t > 0}}\]$ of sub-fields satisfying the usual conditions. The following results are obtained: for $\[f \in BMO\]$, we have $\[f = g - h\]$ with $\[g,h \in BLO\]$; if in addition, f satisfies
then for $\[s > 0\]$ arbitrary, g,h can be chosen such that $\[g,h \in BLO\]$, and
$$\[E({\varepsilon ^{(a - \varepsilon )(g - {g_t})}}|{F_t}) \le {C_{a,\beta ,\varepsilon }},E({\varepsilon ^{(\beta - \varepsilon )(h - {h_t})}}|{F_t}) \le {C_{a,\beta ,\varepsilon }}\]$$
and for weights z, we have
$\[z \in {A_p} \cap S \Leftrightarrow z = {z_1}z_2^{1 - p}\]$ with $\[{z_i} \in {A_i} \cap S,i = 1,2\]$,
where $\[S = \{ \begin{array}{*{20}{c}}
{weight}&{z:C{z_{{T^ - }}} \le {z_T} \le C{z_{{T^ - }}}}
\end{array}\} \]$, $\[\forall \]$ stopping times T, outside a null set }. |
Keywords： |
|
Classification： |
|
|
|
Download PDF Full-Text
|
|
|
|
