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Martingale Operators and Hardy Spaces with Continuous Time Generated by Them

Author

Listed:
  • Zhiwei Hao

    (School of Mathematics and Statistics, Hunan University of Science and Technology, Xiangtan 411201, China)

  • Jianlan Yue

    (School of Mathematics and Statistics, Hunan University of Science and Technology, Xiangtan 411201, China)

  • Ferenc Weisz

    (Department of Numerical Analysis, Eötvös L. University, Pázmány P. Sétány 1/C, 1117 Budapest, Hungary)

Abstract

In this paper, we introduce the martingale Hardy spaces and B M O spaces generated by an operator T in continuous time and establish the atomic decomposition theorem of the space H p T under the condition that T is predictable. We show that the B M O q spaces generated by the operator T are all equivalent and consider the sharp operator. Using the real interpolation method, we identify the interpolation spaces between the Hardy spaces and the B M O spaces. With the aid of atomic decomposition, we establish some martingale inequalities between the Hardy spaces generated by two different operators.

Suggested Citation

  • Zhiwei Hao & Jianlan Yue & Ferenc Weisz, 2025. "Martingale Operators and Hardy Spaces with Continuous Time Generated by Them," Mathematics, MDPI, vol. 13(16), pages 1-19, August.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:16:p:2583-:d:1723021
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    References listed on IDEAS

    as
    1. Pal, Soumik & Protter, Philip, 2010. "Analysis of continuous strict local martingales via h-transforms," Stochastic Processes and their Applications, Elsevier, vol. 120(8), pages 1424-1443, August.
    2. Fan, Ming, 2004. "Some inequalities for p-variations of martingales," Stochastic Processes and their Applications, Elsevier, vol. 109(2), pages 189-201, February.
    3. Soumik Pal & Philip Protter, 2007. "Analysis of continuous strict local martingales via h-transforms," Papers 0711.1136, arXiv.org, revised Jun 2010.
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