On composition operator in the algebra of functions of two variables with bounded total Φ-variation in Schramm sense

• Autorzy: Ereu T. , Merentes N. , Rzepka B. , Sanchez J. L.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

function of two variables; sense of Schramm; Banach algebra; composition operator; left-left regularization

PL

funkcje dwóch zmiennych; algebra Banacha; wariacja ograniczona

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2010
• Tom: Vol. 33
• Strony: 35--50
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Ereu T.

autor

Merentes N.

autor

Rzepka B.

autor

Sanchez J. L.

• Universidad Nacional Abierta, Centro Local Lara (Barquisimeto)-Venezuela,

Bibliografia

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• [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.