## Atomic decompositions of Lorentz martingale spaces and applications.(English)Zbl 1173.60320

Summary: We present three atomic decomposition theorems of Lorentz martingale spaces. With the help of atomic decomposition we obtain a sufficient condition for sublinear operator defined on Lorentz martingale spaces to be bounded. Using this sufficient condition, we investigate some inequalities on Lorentz martingale spaces.

### MSC:

 60G42 Martingales with discrete parameter 60G46 Martingales and classical analysis
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