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Uniformly continuous composition operator in the space of functions of two variables of Bounded ɸ-variation in the sense of Schramm

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We prove in this paper that if the composition operator H, generated by a function h : I b a x C(Iba) Y , maps ɸBV (Iba ,C) into ɸ2 BV (Iba , Y ) and is uniformly continuous, then the left-left regularization h* of h is an affine function with respect to the third variable.
Twórcy
autor
  • Universidad de los Andes, Departamento de Física y Matemáticas, Trujillo-Venezuela
autor
  • Escuela de Matemáticas, Caracas, Venezuela
autor
  • Escuela de Matemáticas, Caracas, Venezuela
  • Escuela de Matemáticas, Caracas, Venezuela
autor
  • Jan Długosz University, Institute of Mathematics and Computer Science, 42-200 Czestochowa, Al. Armii Krajowej 13/15, Poland
Bibliografia
  • [1] H. Nakano, Modulared Semi-Ordered Spaces, Tokyo, 1950.
  • [2] Uniformly continuous composition operators in the space of functions of two variables of bounded φ-variation in the sense of Wiener, Comment. Math., 50(1), (2010), 41-48.
  • [3] J. Appell, P. P. Zabrejko, Nonlinear Superposition Operator, Cambridge University Press, New York, 1990.
  • [4] J. Matkowski, A. Matkowska and N. Merentes, Remark on Globally Lipschitzian Composition Operators, Demostratio. Math. 427(1), (1995), 1, 171-175.
  • [5] J. Matkowski, Lipschitzian composition operators in some function spaces, Nonlinear Anal. 3 (1997), 719-726.
  • [6] J. Matkowski and N. Merentes, Characterization of Globally Lipschitzian Composition Operators in the Sobolev Space Wn p [a, b], Zeszyty Nauk. Politech. Łódzkiej, Mat. 24 (1993), 90-99.
  • [7] J. Matkowski, On Nemytskij Operators, Math. Japonica 33(1), (1988), 81-86.
  • [8] J. Matkowski, J. Mis, On a Characterization of Lipschitzian Operators of Substitution in the Space BV ha, bi, Math. Nachr. 117 (1984), 155-159.
  • [9] M. Kuczma, An Introduction to the Theory of Functional Equations and Inequalities, Polish Scientific Editors and Silesian University, Warszawa-Kraków-Katowice, 1985.
  • [10] M. Schramm, Funtions of ɸ-bounded Variation and Riemann-Stieltjes integration, Transaction Amer. Math. Soc. 267 (1985), 49-63.
  • [11] N. Merentes, S. Rivas, On Characterization of the Lipschitzian Composition Operators between Spaces of Functions of Bounded p-variation, Czechoslovak Mathematical Journal 45(120), (1995), 627-637.
  • [12] N. Wiener, The quadratic variation of function and its Fourier coefficients, Massachusett J. Math. 3 (1924), 72-94.
  • [13] T. Ereú, N. Merentes, J. L. Sánchez, Some remarks on the algebra of functions of two variables with bounded total ɸ-variation in Schramm sense, Comment. Math 50(1), (2010), 23-33.
  • [14] T. Ereú, N. Merentes, B. Rzepka, J. L. Sánchez, On composition in the algebra of functions of two variables with bounded total ɸ-variation in Schramm sense, J. Math. Appl. 33 (2010), 01-15.
  • [15] W. Aziz, N. Merentes, J. L. Sánchez, Regularized Functions on the Plane and Nemytskij Operator, Preprint.
  • [16] W. A. Luxemburg, Banach Function Spaces, Ph.D. Thesis, Technische Hogeschool te Delft, Netherlands, 1955.
  • [17] W. Orlicz, A note on modular spaces. I, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 9 (1961), 157-162.
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Bibliografia
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