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Abstrakty
In this paper we consider the so called composition operator being a self-mapping of the Banach algebra of the function of two variables with bounded total Φ-variation in the Schramm sense. The main result of the paper characterizes the composition operator mentioned above which has a generating function being Lipschitzian with respect to the second variable. The basic tool used in our considerations is the concept of the left-left regularization.
Czasopismo
Rocznik
Tom
Strony
35--50
Opis fizyczny
Bibliogr. 11 poz.
Twórcy
autor
autor
autor
autor
- Universidad Nacional Abierta, Centro Local Lara (Barquisimeto)-Venezuela, tomasereu@gmail.com
Bibliografia
- [1] J. Appel, P. P. Zabrejko, Nonlinear Superposition Operators, Cambridge University Press, New York, 1990.
- [2] V. V. Chistyakov, Mappings of generalized variation and composition operators, Journal of Mathematical Sciences 110, no. 2 (2002), 2455 - 2466.
- [3] V. V. Chistyakov, O. E. Galkin, Mappings of bounded ?-variation with arbitrary functions ?, Journal of Dynamical and Control Systems 4, no. 2 (1998), 217 -247.
- [4] T. Ereú, N. Merentes, J. L. Sánchez, Some remarks on the algebra of functions of two variables with bounded total ?-variation in Schramm sense (preprint).
- [5] T. H. Hildebrandt, Introduction to the Theory of Integration, Academic Press, New York, 1963.
- [6] J. Matkowski, A. Matkowska, N. Merentes, Remark on globally Lipschitzian composition operators, Demonstratio Math. 28, no. 1 (1995), 171 - 175.
- [7] J. Matkowski, Lipschitzian composition operators in some function spaces, Nonlinear Anal. 30 (1997), 719 - 726.
- [8] N. Merentes, Composition operators of functions of bounded ?-variation, P.U.M.A. Ser. 1 (1991), 39 - 45.
- [9] N. Merentes, J. Sánchez, W. Aziz, J. Guerrero, El Espacio de Banach de las funciones regularizadas en R2 (preprint) (2009).
- [10] J. L. Sánchez, A generalization of functions with bounded variation in the Schramm sense, Dep. Math, Central Univ. Venezuela, Caracas, 2008.
- [11] M. Schramm, Functions of ?-bounded variation and Riemann-Stieltjes integration, Transaction Amer. Math. Soc. 287 (1985), 49 - 63.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA7-0043-0023