鞅Hardy空间与Hardy-Orlicz空间的鞅变换

鞅Hardy空间与Hardy-Orlicz空间的鞅变换

Martingale Transforms between Hardy Spaces and Hardy-Orlicz Spaces of Martingales

摘要/Abstract

参考文献

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数学物理学报 ›› 2010, Vol. 30 ›› Issue (6): 1523-1527.

孟维维|于林

三峡大学理学院湖北宜昌 443002

收稿日期:2009-06-06 修回日期:2010-10-15 出版日期:2010-12-25 发布日期:2010-12-25
基金资助:
湖北省高等学校自然科学研究计划重点项目(D200613001)资助

MENG Wei-Wei, YU Lin

College of Science, China Three Gorges University, Hubei Yichang 443002

Received:2009-06-06 Revised:2010-10-15 Online:2010-12-25 Published:2010-12-25
Supported by:
湖北省高等学校自然科学研究计划重点项目(D200613001)资助

摘要：

利用鞅变换, 刻画了鞅Hardy空间与Hardy-Orlicz空间之间的相互关系: 当 $p_\Phi<+\infty$ 时, 证明了Hardy-Orlicz空间 $H^{s}_{\Phi}$ 中的鞅是Hardy空间 $H^{s}_{1}$ 中的鞅变换; 反之, $H^{s}_{1}$ 中的鞅也是 $H^{s}_{\Phi}$ 中的鞅变换.所得结果推广了已有文献中的相应结论.

关键词: 鞅变换, 鞅Hardy空间, 鞅Hardy-Orlicz空间

Abstract:

The martingale transform techniques are used to show that, given any Young function Φ with finite power p_Φ, the corresponding Hardy-Orlicz space H^s_Φis the martingale transform of Hardy spaces H_s¹, and the converse result is also true. The results obtained here extend the
corresponding results in literature.

Key words: Martingale transform, Hardy spaces, Hardy-Orlicz spaces

中图分类号:

60G42

孟维维, 于林. 鞅Hardy空间与Hardy-Orlicz空间的鞅变换[J]. 数学物理学报, 2010, 30(6): 1523-1527.

MENG Wei-Wei, YU Lin. Martingale Transforms between Hardy Spaces and Hardy-Orlicz Spaces of Martingales[J]. Acta mathematica scientia,Series A, 2010, 30(6): 1523-1527.

[1] Burkholder D L. Martingale transforms. Ann Math Stat, 1966, 37: 1494--1504

[2] Garsia A M. Martingale Inequalities. Mathematics Lecture Notes Series. London: W A Benjamin, 1973

[3] Chao K A, Long R L. Martingale transforms and Hardy spaces. Probab Th Rel Fields, 1992, 91: 399--404

[4] Ishak S, Mogyorodi J. On the ${\mathcal {D}}_{\Phi}$ -spaces and the generalization of Herz's and Fefferman's inequality I. Studia Scientiarum Mathematicarum Hungarica, 1982, 17: 229--234

[5] Long R L. Martingale Spaces and Inequalities. Beijing: Peking University Press, 1993

[6] Weisz F. Martingale Hardy Spaces and their Applications in Fourier Analysis. Lecture Notes in Mathematics (1568). Berlin, Heidelberg: Springer-Verlag, 1994

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