A convergence result for unconditional series in Lp(μ)

• Medina, Juan M. ^[1] ; Cernuschi-Frías, Bruno ^[1]
  1. [1] Universidad de Buenos Aires

     Universidad de Buenos Aires

     Argentina

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 32, Nº. 4, 2013, págs. 305-319
• Idioma: inglés
• DOI: 10.4067/S0716-09172013000400001
• Enlaces
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• Resumen

  • We give sufficient conditions for the convergence almost everywhere of the expansion with respect to an unconditional basis for functions in Lp p > 2. This result extends the classical theorem of Menchoff and Rademacher for orthogonal series in L2.

• Referencias bibliográficas
  • Citas [1] Alexits G. , Convergence Problems of Orthogonal Series, Pergamon Press, (1961).
  • [2] Bennett, G. Unconditional Convergence and Almost Everywhere Convergence Z. Wahrs. verw. Gebeite Vol. 34, pp. 135-155, (1976).
  • [3] Gerre, S., Classical Sequences in Banach Spaces, Marcel Dekker, (1992).
  • [4] Houdré C. On the almost sure convergnece of series of satationary and related nonstationary variables, Ann. of Prob. Vol. 23 (3), pp....
  • [5] Kahane J. P. Some Random Series of Functions, Cambridge, (1993).
  • [6] Lindenstrauss J. Tzafriri L. Classical Banach Spaces, Vol. I y II, Springer Verlag 2ed., (1996).
  • [7] Loéve M., Probability Theory, Vol. I, Springer Verlag, (1977).
  • [8] Medina J. M. , Cernuschi -Frías B. Random series in Lp(X, Σ, µ) using Unconditional Basic Sequences and l p stable sequences: A result...
  • [9] Menchoff D. Sur les séries de fonctions orthogonales I., Fund. Math. 4, 1923, pages 82-105. Vol. 40 (2), September, pp. 1490-1503, (1994).
  • [10] Móricz F., Tándori K. An Improved Menshov-Rademacher Theorem, Proc. A. M. S. Vol. 124 (3), pp. 877-885, (1996).
  • [11] Ørno P. A note on Unconditionally converging series in ¨ Lp, Proc. A. M. S. Vol. 59 (2), 252-254, (1976). Lecture Notes in Mathematics...
  • [12] Wojtaszczyk P. Banach Spaces for Analysts, Cambridge, (1996).
  • [13] Yang L., Unconditional Basic Sequence in Lp(µ) and its l p stability, Proc. A. M. S. Vol. 127(2), pp. 455-464, (1999).
  • [14] Zygmund A., Trigonometric Series, Vol II. Cambridge, (1958).