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On complemented subspaces of H 1 and VMO

Part of the Lecture Notes in Mathematics book series (LNM,volume 1376)

Abstract

We prove a Rosenthal-type inequality for some sequences of independent random variables in BMO. This leads to (isomorphically) new complemented subspaces of H 1(δ), one of which is also translation invariant.

This inequality is used also to show that a complemented subspace of H 1 (resp. VMO) either contains a copy of l 2 or is isomorphic to a complemented subspace of (Σ H 1n )1 (resp. (ΣBMO n)co). We thus verify a conjecture of P. Wojtaszczyk.

We also show that Hilbertian subspaces of VMO are complemented, and that the Walsh functions of multiplicity k, k≥2, span uncomplemented copies of l 2 in H 1.

Keywords

  • Independent Random Variable
  • Weizmann Institute
  • Walsh Function
  • Hilbertian Subspace
  • Theoretical Mathematic

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Supported by Erwin Schrödinger-Auslandsstipendium Pr. Nr. J0288P.

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© 1989 Springer-Verlag

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Müller, P.F.X., Schechtman, G. (1989). On complemented subspaces of H 1 and VMO . In: Lindenstrauss, J., Milman, V.D. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 1376. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090051

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  • DOI: https://doi.org/10.1007/BFb0090051

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51303-2

  • Online ISBN: 978-3-540-46189-0

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