Locally defined operators in the space of functions of bounded Λ-variation
Keywords:
Function of bounded Λ-variation, local operator, Nemytskii operator, continuous function
Abstract
We prove that every locally defined operator mapping the space of continuous and bounded Λ-variation functions into itself is a Nemytskii composition operator.
References
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W. Aziz, J. A. Guerrero, K. Maldonado and N. Merentes. Locally defined operators in the space of continuous functions of bounded Riesz-variation, Journal of Mathematics, Volume 2015, Article ID 925091, http://dx.doi.org/10.1155/2015/925091.
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J. Matkowski and M. Wrobel. Locally defined operators in the space of Whitney differentiable functions. Nonlinear Anal., 68 (2008), 2873–3232.
J. Matkowski and M. Wrobel. Representation theorem for locally defined operators in the space of Whitney differentiable functions. Manuscripta Math., 129 (2009), 437–448.
J. Matkowski and M. Wrobel. The bounded local operators in the Banach space of Hölder functions. Jan D lugosz University in Czȩstochowa, Scientific Issues, Mathematics XV (2010), 91–98.
D. Waterman. On convergence of Fourier series of functions of generalized variation. Studia Math., 44 (1972), 107–117.
M. Wrobel. Locally defined operators and a partial solution of a conjecture. Nonlinear Anal., 72 (2010), 495–506.
M. Wrobel. Representation theorem for local operators in the space of continuous and monotone functions. J. Math. Anal. Appl., 372 (2010), 45–54.
M. Wrobel. Locally defined operators in the Hölder’s spaces. Nonlinear Anal., 74 (2011), 317–323.
M. Wrobel. Locally defined operators in the space of functions of bounded φ-variation. Real Anal. Exch., 38(1) (2013), 79–94.
J. Appell and P. P. Zabrejko. Nonlinear superposition operators. Cambridge-Port Chester-Melbourne-Sydney, 1990.
W. Aziz, J. A. Guerrero, K. Maldonado and N. Merentes. Locally defined operators in the space of continuous functions of bounded Riesz-variation, Journal of Mathematics, Volume 2015, Article ID 925091, http://dx.doi.org/10.1155/2015/925091.
K. Lichawski, J. Matkowski and J. Miś. Locally defined operators in the space of differentiable functions. Bull. Pol. Acad. Sci. Math., 37 (1989), 315–325.
J. Matkowski and M. Wrobel. Locally defined operators in the space of Whitney differentiable functions. Nonlinear Anal., 68 (2008), 2873–3232.
J. Matkowski and M. Wrobel. Representation theorem for locally defined operators in the space of Whitney differentiable functions. Manuscripta Math., 129 (2009), 437–448.
J. Matkowski and M. Wrobel. The bounded local operators in the Banach space of Hölder functions. Jan D lugosz University in Czȩstochowa, Scientific Issues, Mathematics XV (2010), 91–98.
D. Waterman. On convergence of Fourier series of functions of generalized variation. Studia Math., 44 (1972), 107–117.
M. Wrobel. Locally defined operators and a partial solution of a conjecture. Nonlinear Anal., 72 (2010), 495–506.
M. Wrobel. Representation theorem for local operators in the space of continuous and monotone functions. J. Math. Anal. Appl., 372 (2010), 45–54.
M. Wrobel. Locally defined operators in the Hölder’s spaces. Nonlinear Anal., 74 (2011), 317–323.
M. Wrobel. Locally defined operators in the space of functions of bounded φ-variation. Real Anal. Exch., 38(1) (2013), 79–94.
Published
2019-12-29
How to Cite
Aziz, W., Guerrero, J. A., & Zambrano, N. (2019). Locally defined operators in the space of functions of bounded Λ-variation. Divulgaciones Matemáticas, 20(2), 31-38. Retrieved from https://produccioncientifica.luz.edu.ve/index.php/divulgaciones/article/view/36628
Section
Research papers
