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L~Φ可料控制鞅Hardy-Orlicz空间之间的鞅变换 被引量：3

Martingale Rransforms between Hardy-Orlicz Spaces of L~ΦPredictable Martingales
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摘要 以鞅变换为工具，刻画了LФ可料控制鞅的Hardy-Orlicz空间之间的相互关系，设Ф1和Ф2是两个Young函数，并在某种意义上Ф2强于Ф1（具体定义见正文），以构造性的方法证明了Hardy—Orlicz空间DФ1中的Ф恰好是Hardy-Orlicz空间要强DФ2的鞅的鞅变换．所得的结果推广了已有文献中的相关结论． Using the technique of martingale transforms, the relation between Hardy-Orlicz spaces of LФpredictable martingales is investigated. Let Ф1 and Ф2 be two Young functions and Ф1 - Ф2 in some sense, a constructive proof is obtained of that the elements in Hardy-Orlicz space DФ1 are none other than the martingale transforms of those in Hardy-Orlicz space DФ2. The results obtained here extend the corresponding results in the former literatures.
作者 罗锋 于林 郭红萍
机构地区 三峡大学理学院
出处 《应用泛函分析学报》 CSCD 2012年第3期245-250,共6页 Acta Analysis Functionalis Applicata
基金 湖北省自然科学基金(2010CDB10807) 湖北省教育厅自然科学研究计划重点项目(D20101204)
关键词 鞅变换 YOUNG函数 鞅Hardy—Orlicz空间 martingale transforms Young functions Hardy-Orlicz spaces
分类号 O177.2 [理学—基础数学] O211.6 [理学—概率论与数理统计]
  • 相关文献

参考文献9

  • 1Burkholder D L. Martingale transforms[J]. Ann of Math, 1966, 6(37): 1494-1504.
  • 2Garsia A M. Martingale inequalities[M], In: Seminar Notes on Recent Progress. In: Mathematics Lecture Notes Series, W A Benjamin, Inc., Reading. 1973.
  • 3Weisz F. Hardy spaces of predictable martingales[J]. Analysis Mathematica, 1994, 20(3): 225-233.
  • 4CHAO K A, LONG R L. Martingale transforms and Hardy spacesJ]. Probability Theory and Related Fields, 1992, 91: 399-404.
  • 5LONG R L. Martingale Spaces and Inequalities[M]. Beijing, Peking University Press and Vieweg Pub- lishing, Braunschweig, Wiesbaden, 1993.
  • 6Weisz F. Martingale Hardy Spaces and Their Applications in Fourier Analysis[M]. In: Lecture Notes in Mathematics, vol. 1568. Springer, Berlin, 1994.
  • 7Ishak S, Mogyorddi J. On the-spaces and the generalization of Herz's and Fefferman's inequality I[J]. Studia Scientiarum Mathematicarum Hungarica, 1982, 17: 229-234.
  • 8MENG W W, YU L. Martingale transform between 1 and v of martingale spaces[J]. Statistics and Probability Letters, 2009, 79(22): 2328-2333.
  • 9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（A辑）,2010,30(6):1523-1527. 被引量：2

二级参考文献6

  • 1Burkholder D L.Martingale transforms.Ann Math Stat,1966,37:1494-1504.
  • 2Garsia A M.Martingale Inequalities.Mathematics Lecture Notes Series.London:W A Benjamin,1973.
  • 3Chao K A,Long R L.Martingale transforms and Hardy spaces.Probab Th Rel Fields,1992,91:399-404.
  • 4Ishak S,Mogyorodi J.On the Dφ-spaces and the generalization of Herz's and Fefferman's inequality Ⅰ.Studia Scientiarum Mathematicarum Hungarica,1982,17:229-234.
  • 5Long R L.Martingale Spaces and Inequalities.Beijing:Peking University Press,1993.
  • 6Weisz F.Martingale Hardy Spaces and their Applications in Fourier Analysis.Lecture Notes in Mathematics (1568).Berlin,Heidelberg:Springer-Verlag,1994.

共引文献1

同被引文献24

  • 1Burkholder D L. Distribution function inequalities for martingMes. The Annals of Probability, 1973, 1(1): 19-42.
  • 2Bassily N L, Abdel-Fattah A M. On the duality of some martingale spaces. Bull Austral Math Soc, 1992, 45:43-52.
  • 3Chao J A, Long R L. Martingale transforms with unbounded multipliers. Proceedings of the American Mathematical Society, 1992, 114(3): 831-838.
  • 4Chao J A, Long R L. Martingale transforms and Hardy spaces. Probability Theory and Related Fields, 1992, 91:399-404.
  • 5Dam B K. The dual of the martingale Hardy space T/ with general Young function 4. Analysis Mathe- matica, 1988, 14:287-294.
  • 6Dam B K. General form of linear functionals on Hardy spaces. Acta Mathcmatica Vietnamica, 2003, 28(3): 259-266.
  • 7Garsia A M. Martingale Inequalities. Seminar Notes on Recent Progress. Mathematics Lecture Notes Series. New York: Benjamin Inc, 1973.
  • 8Ishak S, MogyorSdi J. On the -spaces and the generalization of Herz's and Feffcrman's inequality I. Studia Scientiarum Mathematicarum Hungarica, 1982, 7:229-234.
  • 9Meng W W, Yu L. Martingale transform between Q1 and QI, of martingale spaces. Statistics and Proba- bility Letters, 2009, 79:2328-2333.
  • 10Weisz F. Hardy spaces of predictable martingales. Analysis Mathematica, 1994, 20:225-233.

引证文献3

二级引证文献3

应用泛函分析学报
2012年 第3期

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