Abstract
We introduce the martingale Morrey spaces built on Banach function spaces. We establish the Doob's inequality, the Burkholder-Gundy inequality and the boundedness of martingale transforms for our martingale Morrey spaces. We also introduce the martingale block spaces. By the Doob's inequality on martingale block spaces, we obtain the Davis' decompositions for martingale Morrey spaces. Copyright © 2018 Wuhan Institute of Physics and Mathematics. Published by Elsevier Ltd. All rights reserved.
| Original language | English |
|---|---|
| Pages (from-to) | 93-109 |
| Journal | Acta Mathematica Scientia |
| Volume | 38 |
| Issue number | 1 |
| Early online date | Dec 2017 |
| DOIs | |
| Publication status | Published - 2018 |
Citation
Ho, K.-P. (2018). Doob's inequality, Burkholder-Gundy inequality and martingale transforms on martingale Morrey spaces. Acta Mathematica Scientia, 38(1), 93-109. doi: 10.1016/S0252-9602(17)30119-4Keywords
- Morrey spaces
- Banach function space
- Block spaces
- Doob's inequality
- Burkholder-Gundy inequality
- Martingale transform
- Davis' decomposition
- Martingale