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Interpolation for weak Orlicz spaces with M Δ condition

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Abstract

An interpolation theorem for weak Orlicz spaces generalized by N-functions satisfying M Δ condition is given. It is proved to be true for weak Orlicz martingale spaces by weak atomic decomposition of weak Hardy martingale spaces. And applying the interpolation theorem, we obtain some embedding relationships among weak Orlicz martingale spaces.

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References

  1. Fefferman R, Soria F. The space weak H 1. Studia Math, 85: 1–16 (1987)

    MathSciNet  Google Scholar 

  2. Weisz F. Weak martingale Hardy spaces. Probab Math Statist, 18: 133–148 (1998)

    MATH  MathSciNet  Google Scholar 

  3. Weisz F. Bounded operator on weak Hardy spaces and applications. Acta Math Hungar, 80(3): 249–264 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  4. Bennett C. Weak-L ∞ and BMO. Ann of Math, 113: 601–611 (1981)

    Article  MathSciNet  Google Scholar 

  5. Jawerth B, Milman M. Interpolation of weak type spaces. Math Z, 201: 509–519 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  6. Feher F, Strauss M J. Weak type interpolation and orbits. Comput Math Appl, 3-6(30): 417–431 (1995)

    Article  MathSciNet  Google Scholar 

  7. Liu P D, Hou Y L, Wang M F. Weak Orlicz space and its applications to martingale theory. Studia Math, to appear

  8. Hou Y L, Ren Y B. Weak martingale Hardy spaces and weak atomic decompositions. Sci China Ser A-Math, 49(7): 912–921 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  9. Rao M M, Ren Z D. Theory of Orlicz Spaces. New York: Mercel Dekker, 1991

    MATH  Google Scholar 

  10. Wu C X, Wang T F. Orlicz Spaces and it Applications (in Chinese). Harbin: Heilongjiang Science & Technology Press, 1983

    Google Scholar 

  11. Weisz F. Martingale Hardy spaces and its applications in Fourier analysis. Lecture Notes in Math, Vol. 1568. Berlin: Springer-Verlag, 1994

    Google Scholar 

  12. Long R L. Martingale Spaces and Inequalities. Beijing: Peking University Press, 1993

    MATH  Google Scholar 

  13. Bergh J, Lofstrom J. Interpolation Spaces. Berlin: Springer-Verlag, 1976

    MATH  Google Scholar 

Download references

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Authors and Affiliations

  1. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China

    Yong Jiao & PeiDe Liu

  2. Department of Mathematics, Yunyang Teacher College, Shiyan, 442000, China

    LiHua Peng

Authors
  1. Yong Jiao
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  2. LiHua Peng
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  3. PeiDe Liu
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Corresponding author

Correspondence to Yong Jiao.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant No. 10671147)

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Jiao, Y., Peng, L. & Liu, P. Interpolation for weak Orlicz spaces with M Δ condition. Sci. China Ser. A-Math. 51, 2072–2080 (2008). https://doi.org/10.1007/s11425-008-0078-z

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  • DOI: https://doi.org/10.1007/s11425-008-0078-z

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