Martingale Operators and Hardy Spaces with Continuous Time Generated by Them

Zhiwei Hao, Jianlan Yue and Ferenc Weisz ()
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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

Mathematics, 2025, vol. 13, issue 16, 1-19

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.

Keywords: continuous martingales; Hardy spaces; atomic decompositions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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