Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-25T04:14:03.979Z Has data issue: false hasContentIssue false
  • English
  • Français

An Extension of Nikishin’s Factorization Theorem

Published online by Cambridge University Press:  20 November 2018

Geoff Diestel
Geoff Diestel*
Affiliation:
Texas A&M University-Central Texas, 1001 Leadership Place, Killeen TX 76549, USA e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A Nikishin–Maurey characterization is given for bounded subsets of weak-type Lebesgue spaces. New factorizations for linear and multilinear operators are shown to follow.

Keywords

46E3028A25factorizationtypecotypeBanach spaces
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 60 , Issue 1 , 01 March 2017 , pp. 104 - 110
Copyright
Copyright © Canadian Mathematical Society 2017

References

[1] Albiac, F. and Kalton, N., Topics in Banach space theory. Graduate Texts in Mathematics, 233. Springer, New York, 2006.Google Scholar
[2] Diestel, G., Factoring multi-sublinear maps J. Funct. Anal. 266(2014), no. 4,1928-1947. http://dx.doi.Org/10.101 6/j.jfa.2O13.12.010 Google Scholar
[3] Grafakos, L., Classical Fourier analysis. 2nd edition. Graduate Texts in Mathematics, 249. Springer, New York, 2008.Google Scholar
[4] Johnson, W. B. and Lindenstrauss, J., eds. Handbook of the Geometry of Banach Spaces, Vol. 1, North-Holland, Amsterdam, 2001.Google Scholar
[5] Johnson, W. B. and Lindenstrauss, J., Handbook of the geometry of Banach spaces, Vol. 2. North-Holland, Amsterdam, 2001.Google Scholar
[6] Kalton, N. J., Rademacher series and decoupling. New York J. Math. 11(2005), 563–595.Google Scholar
[7] Maurey, B., Théorèmes de factorisation pour les opérateurs linéaires à valeurs dans les espaces Lp. Astérisque, 11. Société Mathématique de France, Paris, 1974.Google Scholar
[8] Nikishin, E. M., Resonance theorems and superlinear operators. Uspekhi Mat. Nauk 25(1970), no. 6(156), 129–191. (Russian.Google Scholar
[9] Pisier, G., Factorization of operators through Lp∞ or Lp\ and noncommutative generalizations. Math. Ann. 276(1986), 105–136. http://dx.doi.Org/10.1007/BF01450929 Google Scholar
[10] Wojtaszczyk, P., Banach spaces for analysts. Cambridge Studies in Advanced Mathematics, 25.Cambridge University Press, Cambridge, 1991. http://dx.doi.Org/!0.1017/CBO9780511608735 Google Scholar