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Martingale hardy spaces for 0<p≦1
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  • Published: September 1990

Martingale hardy spaces for 0<p≦1

  • F. Weisz1 

Probability Theory and Related Fields volume 84, pages 361–376 (1990)Cite this article

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Summary

The relation between the usually considered martingale Hardy spaces is examined. It will be shown that if the stochastic basis is regular, then all these Hardy spaces are equivalent. An atomic description of the spacesH − p andP p will be given for 0<p≦1 and with the help of this we shall consider the duals of these spaces. Moreover, the dual space ofVMO p generated by the dual space ofH −pp will be determined in the case when all σ-algebras are generated by countably many atoms. Furthermore, we shall show in this case that the dual ofVMO 1 isH −1 .

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References

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Authors and Affiliations

  1. Department of Numerical Analysis, University Eötvös Loránd, Muzeum krt. 6-8, H-1088, Budapest, Hungary

    F. Weisz

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  1. F. Weisz
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Weisz, F. Martingale hardy spaces for 0<p≦1. Probab. Th. Rel. Fields 84, 361–376 (1990). https://doi.org/10.1007/BF01197890

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  • Received: 06 June 1988

  • Revised: 20 March 1989

  • Issue Date: September 1990

  • DOI: https://doi.org/10.1007/BF01197890

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Keywords

  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Hardy Space
  • Dual Space
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