In this paper, we investigate several two-parameter weak Orlicz–Hardy martingale spaces generated by the $p$-convex and $q$-concave functions, and establish their atomic decomposition theorems. Using the atomic decomposition, we obtain a sufficient condition for the boundedness of a sublinear operator defined on the two-parameter weak Orlicz–Hardy martingale spaces. Furthermore, the dual spaces of the two-parameter weak Orlicz–Hardy martingale spaces are considered.
Kaituo Liu is supported by the Doctoral Scientific Research Foundation of HuBei University of Automotive Technology Grand BK201805. Jianzhong Lu is supported by the Fundamental Research Funds for the Central University of Central South University (No. 2021zzts0032). Tian Yue is supported by the Science and Technology Research Project of Department of Education of Hubei Province Grand B2021140.
Kaituo Liu. Jianzhong Lu. Jun Wu. Tian Yue. "Orlicz–Hardy Weak Martingale Spaces for Two-parameter." Taiwanese J. Math. Advance Publication 1 - 24, 2023. https://doi.org/10.11650/tjm/230101