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UNIFORMLY BOUNDED COMPOSITION OPERATORS

Published online by Cambridge University Press:聽 30 July 2015

DOROTA G艁AZOWSKA
Affiliation:
Faculty of Mathematics, Computer Science and Econometrics, University of Zielona G贸ra, Szafrana 4a, 65-516 Zielona G贸ra, Poland email D.Glazowska@wmie.uz.zgora.pl
JANUSZ MATKOWSKI
Affiliation:
Faculty of Mathematics, Computer Science and Econometrics, University of Zielona G贸ra, Szafrana 4a, 65-516 Zielona G贸ra, Poland email J.Matkowski@wmie.uz.zgora.pl
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Abstract

We prove that if a uniformly bounded (or equidistantly uniformly bounded) Nemytskij operator maps the space of functions of bounded ${\it\varphi}$ -variation with weight function in the sense of Riesz into another space of that type (with the same weight function) and its generator is continuous with respect to the second variable, then this generator is affine in the function variable (traditionally, in the second variable).

Type
Research Article
Copyright
漏 2015 Australian Mathematical Publishing Association Inc.聽

References

Appell, J. and Zabrejko, P.聽P., Nonlinear Superposition Operators (Cambridge University Press, Cambridge, 1990).CrossRefGoogle Scholar
Armao, F., G艂azowska, D., Rivas, S. and Rojas, J., 鈥Uniformly bounded composition operators in the Banach space of bounded (p, k)-variation in the sense of Riesz鈥揚opoviciu鈥, Cent. Eur. J. Math. 11(2) (2013), 357367.Google Scholar
Aziz, W., Azocar, A., Guerrero, J. and Merentes, N., 鈥Uniformly continuous composition operators in the space of functions of 饾湙-variation with weight in the sense of Riesz鈥, Nonlinear Anal. 74 (2011), 573576.CrossRefGoogle Scholar
Chistyakov, V. V., 鈥Lipschitzian superposition operators between spaces of functions of bounded generalized variation with weight鈥, J. Appl. Anal. 6(2) (2000), 173186.CrossRefGoogle Scholar
G艂azowska, D., Matkowski, J., Merentes, N. and S谩nchez Hern谩ndez, J. L., 鈥Uniformly bounded composition operators in the Banach space of absolutely continuous functions鈥, Nonlinear Anal. 75(13) (2012), 49955001.CrossRefGoogle Scholar
Kuczma, M., An Introduction to the Theory of Functional Equations and Inequalities (Polish Scientific Editors and Silesian University, Warszawa, Krak贸w, Katowice, 1985).Google Scholar
Lichawski, K., Matkowski, J. and Mi艣, J., 鈥Locally defined operators in the space of differentiable functions鈥, Bull. Polish Acad. Sci. Math. 37 (1989), 315325.Google Scholar
Matkowski, J., 鈥Functional equations and Nemytskij operators鈥, Funkcial Ekvac. 25 (1982), 127132.Google Scholar
Matkowski, J., 鈥Uniformly bounded composition operators between general Lipschitz function normed spaces鈥, Topol. Methods Nonlinear Anal. 38(2) (2011), 395405.Google Scholar
Matkowski, J. and Wr贸bel, M., 鈥Locally defined operators in the space of Whitney differentiable functions鈥, Nonlinear Anal. 68(10) (2008), 29332942.CrossRefGoogle Scholar
Matkowski, J. and Wr贸bel, M., 鈥Representation theorem for locally defined operators in the space of Whitney differentiable functions鈥, Manuscripta Math. 129(4) (2009), 437448.CrossRefGoogle Scholar
Wr贸bel, M., 鈥Locally defined operators and a partial solution of a conjecture鈥, Nonlinear Anal. 72(1) (2010), 495506.CrossRefGoogle Scholar
Wr贸bel, M., 鈥Representation theorem for local operators in the space of continuous and monotone functions鈥, J. Math. Anal. Appl. 372(1) (2010), 4554.CrossRefGoogle Scholar
Wr贸bel, M., 鈥Locally defined operators in H枚lder鈥檚 spaces鈥, Nonlinear Anal. 74(1) (2011), 317323.CrossRefGoogle Scholar

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