Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On local Khintchine inequalities for spaces of exponential integrability

Author: Javier Carrillo-Alanís
Journal: Proc. Amer. Math. Soc. 139 (2011), 2753-2757
MSC (2010): Primary 46E30, 42C10
Published electronically: February 1, 2011
MathSciNet review: 2801616
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove a local version of the Khintchine inequality for the spaces $ {\mathrm{Exp} } L^p([0,1])$ of functions having $ p$-th exponential integrability, for $ 1 \leq p \leq 2$. The result also holds for the lacunary Walsh series.

References [Enhancements On Off] (What's this?)

  • 1. C. Bennett and R. Sharpley, Interpolation of Operators (Academic Press, Boston, 1988). MR 928802 (89e:46001)
  • 2. A. Khintchine, Über Dyadische Brüche, Math. Z. 18 (1923), 109-116. MR 1544623
  • 3. A. Khintchine and A. Kolmogoroff, Über Konvergenz von Reihen, deren Glieder durch den Zufall bestimmt werden, Mat. Sb. 32:4 (1925), 668-677.
  • 4. M. A. Krasnoselskii and Y. Rutickii, Convex Functions and Orlicz Spaces (Noordhoff, Groningen, 1961). MR 0126722 (23:A4016)
  • 5. S. G. Krein, Ju. I. Petunin, and E. M. Semenov, Interpolation of Linear Operators (Amer. Math. Soc., Rhode Island, 1982). MR 649411 (84j:46103)
  • 6. H. Rademacher, Einige Sätze der Reihen von Allgemeinen Orthogonalfunktionen, Math. Ann. 87 (1922), 112-138. MR 1512104
  • 7. V. A. Rodin and E. M. Semenov, Rademacher series in symmetric spaces, Anal. Math. 1 (1975), 207-222. MR 0388068 (52:8905)
  • 8. Y. Sagher and K. Zhou, A Local Version of a Theorem of Khinchin, in: Analysis and Partial Diff. Eq., Lecture Notes in Pure and Appl. Math. 122 (Dekker, New York, 1990), 327-330. MR 1044796 (91e:42039)
  • 9. Y. Sagher and K. Zhou, Exponential Integrability of Rademacher Series, in: Convergence in Ergodic Theory and Probability (de Gruyter, Berlin, 1996), 389-395. MR 1412621 (97k:42018)
  • 10. Y. Sagher and K. Zhou, Local norm inequalities for lacunary series, Indiana Univ. Math. J. 39 (1990), 45-60. MR 1052010 (91b:42017)
  • 11. A. Zygmund, Trigomometric Series (Cambridge University Press, Cambridge, 1977). MR 0617944 (58:29731)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 46E30, 42C10

Retrieve articles in all journals with MSC (2010): 46E30, 42C10

Additional Information

Javier Carrillo-Alanís
Affiliation: Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Apdo. 1160, Sevilla, 41080, Spain

Keywords: Rademacher functions, rearrangement invariant spaces
Received by editor(s): July 13, 2010
Published electronically: February 1, 2011
Additional Notes: Partially supported by D.G.I. #MTM2009-12740-C03-02
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society