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Banach spaces related to α-stable measures

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Probability Theory on Vector Spaces II

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 828))

Abstract

A class Vα of Banach spaces is defined by the inequality (2) for α-stable measures, where 1≤α≤2. It is shown that if α<2 then there exists a Banach space of α-stable type which does not belong to Vα. A characterization of α-stable Radon measure in α-stable spaces from the Vα class is given for 1<α<2.

Partially written during the second author’s stay at Southern Illinois University, Carbondale, IL 62901.

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References

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Author notes

  1. Nguyen Zui Tien

    Present address: Department of Mathematics, University of Hanoi, Hanoi, Vietnam

Authors and Affiliations

  1. Institute of Mathematics, Wroclaw Technical University, 50-370, Wroclaw, Poland

    Nguyen Zui Tien & Aleksander Weron

Authors
  1. Nguyen Zui Tien
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  2. Aleksander Weron
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A. Weron

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© 1980 Springer-Verlag

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Tien, N.Z., Weron, A. (1980). Banach spaces related to α-stable measures. In: Weron, A. (eds) Probability Theory on Vector Spaces II. Lecture Notes in Mathematics, vol 828. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097418

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  • DOI: https://doi.org/10.1007/BFb0097418

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10253-3

  • Online ISBN: 978-3-540-38350-5

  • eBook Packages: Springer Book Archive

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