On functions of bounded (p,2)-variation

• Autores: Nelson Merentes
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 43, Fasc. 2, 1992, págs. 117-123
• Idioma: inglés
• Títulos paralelos:
  • Sobre funciones de (p,2)-variación acotada
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• Resumen

  • In this paper we introduce the concept of $(p,2)$-variation which generalizes the Riesz $p$-variation. The following result is proved: A function $f:[a,b]\rightarrow\mathbb{R}$ is of bounded $(p,2)$-variation $(1 < p <\infty)$ if and only if f' is absolutely continuous on $[a,b]$ and $f''\in L_p[a,b]$. Moreover it is shown that the $(p,2)$-variation of a function $\int$ on [a,b] is given by $$V^2_p(f;[a,b])=\parallel f''\parallel^p_{L_p}[a,b]^\cdot$$

• Referencias bibliográficas
  • E. Hewitt and K. Stromberg, Real and Abstract Analysis, Springer, 1965.
  • C. Jordan, Sur la série de Fourier, C. R. Acad. Sci. Paris 92 (1881), 228–230.
  • F. Riesz, Untersuchungen über Systeme integrierbarer Functionen, Mathematische Annalen. 69 (1910), 449–497.
  • A.M. Russell, Functions of bounded second variation and Stieltjes-type integrals, J. London Math. Soc. 2, 2 (1970), 193–203.
  • Ch.J. de la Vallée Poussin, Sur la convergence des formules d’interpolation entre ordonnées équidistantes, Bull. Acad. Sci. Belg. (1908),...