Remarks on uniformly bounded composition operator acting between Banach spaces of functions of two variables of bounded schramm Φ-variation

• Autorzy: Ereú T. , Merentes N. , Wróbel M.
• Języki publikacji: EN

Abstrakty

EN

In this paper we prove that if the composition operator H of generator h : I^b_a × C → Y (X is a real normed space, Y is a real Banach space, C is a convex cone in X and I^b_a ⸦ R²) maps Φ₁ BV (I^b_a, C) into Φ₂ BV (I^b_a, Y) and is uniformly bounded, then the left-left regularization h* of h is an affine function in the third variable.

Słowa kluczowe

EN

composition operator; affine function

PL

operator kompozycji; funkcja ograniczona

• Wydawca: Wydawnictwo Uniwersytetu Humanistyczno-Przyrodniczego im. Jana Długosza w Częstochowie
• Czasopismo: Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
• Rocznik: 2013
• Tom: Vol. 18
• Strony: 19--27
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Ereú T.

• Universidad Central de Venezuela, Escuela de Matemáticas, Caracas, Venezuela

autor

Merentes N.

• Universidad Central de Venezuela, Escuela de Matemáticas, Caracas, Venezuela

autor

Wróbel M.

• Jan Długosz University, Institute of Mathematics and Computer Science, 42-200 Częstochowa, Al. Armii Krajowej 13/15, Poland

Bibliografia

• [1] W. Aziz, T. Ereu, N. Merentes, J. L. Sanchez, M. Wrobel, Uniformly continuous operators in the space of functions of two variables of bounded Φ-variation in the sense of Schramm, Scientific Issues, Jan Długosz University in Częstochowa, Mathematics XVII (2012), 7-16.
• [2] T. Ereu, N. Merentes, J. L. Sanchez, Some remarks on the algebra of functions of two variables with bounded total Φ-variation in Schramm sense, Comment. Math 50(1), (2010), 23–33.
• [3] T. Ereu, N. Merentes, B. Rzepka and J. L. Sanchez, On composition in the algebra of functions of two variables with bounded total Φ-variation in Schramm sense, J. Math. Appl., 33 (2010), 01-15.
• [4] M. Kuczma, An Introduction to the Theory of Functional Equations and Inequalities, Polish Scientific Editors and Silesian University, Warszawa-Krakow-Katowice, 1985.
• [5] W. A. Luxemburg, Banach Function Spaces, Ph.D. Thesis, Technische Hogeschool te Delft, Netherlands, 1955.
• [6] J. Matkowski, Uniformly bounded composition operators between general Lipschitz functions normed spaces, Topol. Methods Nonlinear Anal., 38(2) (2011), 395-406.
• [7] H. Nakano, Modulared Semi-Ordered Spaces, Tokyo, 1950.
• [8] M. Schramm, Funtions of Φ-Bounded Variation and Riemann-Stieltjes integration, Transaction Amer. Math. Soc., 267, (1985), 49-63.