Martingale transforms in martingale Hardy spaces with variable exponents

Tao Ma; Jianzhong Lu; Xia Wu; Tao Ma; Jianzhong Lu; Xia Wu

doi:10.3934/math.20241071

AIMS Mathematics

2024, Volume 9, Issue 8: 22041-22056. doi: 10.3934/math.20241071

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Martingale transforms in martingale Hardy spaces with variable exponents

Tao Ma ¹,
Jianzhong Lu ^{2
,
,},
Xia Wu ²

1.
School of Mathematics and Statistics, South-Central Minzu University, Wuhan 430072, China
2.
School of Mathematics and Information, Xiangnan University, Chenzhou 423000, China

Received: 31 May 2024 Revised: 27 June 2024 Accepted: 01 July 2024 Published: 15 July 2024
MSC : 60G42, 60G46

In this paper, we considered the boundedness of Burkholder's martingale transforms for martingale Hardy spaces with variable exponents. In addition, through martingale transforms, some characterizations of predictable variable exponent martingale Hardy spaces were also provided.
- variable exponent,
- martingale Hardy space,
- martingale transform,
- Doob's maximal inequality,
- Lipschitz space
Citation: Tao Ma, Jianzhong Lu, Xia Wu. Martingale transforms in martingale Hardy spaces with variable exponents[J]. AIMS Mathematics, 2024, 9(8): 22041-22056. doi: 10.3934/math.20241071

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Abstract

In this paper, we considered the boundedness of Burkholder's martingale transforms for martingale Hardy spaces with variable exponents. In addition, through martingale transforms, some characterizations of predictable variable exponent martingale Hardy spaces were also provided.

References

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