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http://yadda.icm.edu.pl:80/baztech/element/bwmeta1.element.baztech-article-BUS8-0012-0002

Czasopismo

Commentationes Mathematicae

Tytuł artykułu

A Representation Theorem for '-Bounded Variation of Functions in the Sense of Riesz

Autorzy Aziz, W.  Leiva, H.  Merentes, N.  Rzepka, B. 
Treść / Zawartość http://wydawnictwa.ptm.org.pl/index.php/commentationes-mathematicae/ http://www.staff.amu.edu.pl/~commath/
Warianty tytułu
Języki publikacji EN
Abstrakty
EN In this paper we extend the well known Riesz lemma to the class of bounded φ-variation functions in the sense of Riesz defined on a rectangle [...].This concept was introduced in [2], where the authors proved that the space [...] of such functions is a Banach Algebra. Moreover, they characterized also the Nemytskii operator acting in this space. Thus our result creates a continuation of the paper [2].
Słowa kluczowe
EN bounded variation   function of bounded variation in the sense of Riesz   variations spaces   Banach space   algebra space  
Wydawca Polskie Towarzystwo Matematyczne
Czasopismo Commentationes Mathematicae
Rocznik 2010
Tom Vol. 50, [Z] 2
Strony 109--120
Opis fizyczny Bibliogr. 16 poz.
Twórcy
autor Aziz, W.
autor Leiva, H.
autor Merentes, N.
autor Rzepka, B.
  • Escuela de Matematicas, Universidad Central de Venezuela Caracas - Venezuela, wadie@ula.ve
Bibliografia
[1] R. Adams and J. A. Clarkson, Properties of functions f(x, y) of bounded variation, Trans. Amer. Math. Soc. 36 (1934), 711-730.
[2] W. Aziz, H. Leiva, N. Merentes and J. Sanchez, Functions of two variables with bounded φ-variation in the sense of Riesz, to appear in J. Math. Appl.
[3] E. Berkson and T. A. Gillespie, Absolutely continuous functions of two variables and wellbounded operators, J. London Math. Soc. 2, no. 30, (1984), 305-321.
[4] V. V. Chistyakov, Superposition operators in the algebra of functions of two variables with finite total variation, Monatshefte Math. 137 (2002), 99-114.
[5] J. A. Clarkson and R. Adams, On definitions of bounded variation for functions of two variables, Trans. Amer. Math. Soc. 35 (1933), 824-854.
[6] C. Jordan, Sur la série de Fourier, C. R. Acad. Sci. Paris Sér. I Math. 92 (1881), 228-230.
[7] S. Łojasiewicz, An Introduction to the Theory of Real Functions, John Wiley & Sons, Chichester, 1988.
[8] Yu. T. Medvedev, Generalization of a theorem of F. Riesz, Uspekhi Mat. Nauk. 6 (1953), 115-118 (in Russian).
[9] N. Merentes and S. Rivas, El Operador de Composición en Espacios de Funciones con algun tipo de Variación Acotada, p. 256, Facultad Ciencias-ULA, Mérida-Venezuela, 1996.
[10] F. Riesz, Untersuchungen ¨uber Systeme integrierbarer Funktionen, Math. Analen 69 (1910), 449-497.
[11] R. T. Seeley, Fubini implica Leibniz fyx = fxy, Amer. Math. Month. 68 (1968), 57-58.
[12] J. Šremr, A note on absolutely continuous functions of two variables in sense of Carath éodory, Instit. of Math., AS CR, Prague (2008), 1-12.
[13] S. Walczak, Absolutely continuous functions of several variables and their applications to differential equations, Bull. Pol. Acad. Sci. Math. 35 (1987), 733-744.
[14] S. Walczak, On the differentiability of absolutely continuous functions of several variables. Remarks on the Rademacher theorem, Bull. Pol. Acad. Sci. Math. 36 (1988), 513-520.
[15] N. Wiener, The quadratic variation of a function and its Fourier coefficients, J. Math. And Phys. 3 (1924), 72-94.
[16] L. C. Young, Sur une généralisation de la notion de variation de puissance p-i`eme borne au sense de M. Wiener, et sur la convergence des séries de Fourier, C. R. Acad. Sci. Paris, 240 (1937), 470-472.
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