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| DOUBLE $\Phi$-FUNCTION INEQUALITY FOR NONNEGATIVE SUBMARTINGALES |
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Citation： |
MEI Tao,LIU Peide.DOUBLE $\Phi$-FUNCTION INEQUALITY FOR NONNEGATIVE SUBMARTINGALES[J].Chinese Annals of Mathematics B,2000,21(2):211~216 |
| Page view： 1061
Net amount： 848 |
Authors： |
MEI Tao; LIU Peide |
Foundation： |
Project supported by the National Natural Science Foundation of China. |
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| Abstract： |
The authors establish a kind of
inequalities for nonnegative submartingales which depend on
two functions $\Phi $ and $\Psi $, and obtain the equivalent conditions
for $\Phi $ and $\Psi$ such that this kind of inequalities holds.
In the case $\Phi=\Psi\in\Delta _2$, it is proved that this necessary and
sufficient condition is equivalent to $q_{\Phi }>1$. |
Keywords： |
Martingale, Nonnegative submartingale, Maximal function, $\Phi$-function
inequality |
Classification： |
60G42, 46E30 |
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