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<p>In this paper, we develop the martingale theory in the framework of the grand Orlicz-Lorentz spaces. Atomic decompositions of the grand Orlicz-Lorentz martingale spaces are established. With the help of the atomic decompositions, the dual spaces of the grand Orlicz-Lorentz martingale spaces are proved to be the generalized BMO martingale spaces. Moreover, by duality we obtain a John-Nirenberg inequality for the generalized BMO martingale spaces when the stochastic basis is regular. The results obtained here generalize the corresponding known results in grand martingale Hardy spaces and various classical martingale Hardy spaces.</p>

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Dual Spaces of Grand Orlicz-Lorentz Martingale Spaces and John-Nirenberg Inequalities

  • 期刊论文

  • 发表日期：

    2025年8月22日

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  • Libo Li,
  • Yao Wang,
  • Anming Yang

摘要

In this paper, we develop the martingale theory in the framework of the grand Orlicz-Lorentz spaces. Atomic decompositions of the grand Orlicz-Lorentz martingale spaces are established. With the help of the atomic decompositions, the dual spaces of the grand Orlicz-Lorentz martingale spaces are proved to be the generalized BMO martingale spaces. Moreover, by duality we obtain a John-Nirenberg inequality for the generalized BMO martingale spaces when the stochastic basis is regular. The results obtained here generalize the corresponding known results in grand martingale Hardy spaces and various classical martingale Hardy spaces.