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Uniformly continuous set-valued composition operators in the space of total phi-bidimensional variation in the sense of Riesz

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EN
Abstrakty
EN
In this paper we prove that if a Nemytskij composition operator, generated by a function of three variables in which the third variable is a function one, maps a suitable large subset of the space of functions of bounded total φ-bidimensional variation in the sense of Riesz, into another such space, and is uniformly continuous, then its generator is an affine function in the function variable. This extends some previous results in the one-dimensional setting.
Rocznik
Strony
241--248
Opis fizyczny
Bibliogr. 18 poz.
Twórcy
autor
autor
autor
  • Universidad de Los Andes Dpto. de Física y Matemáticas Trujillo-Venezuela, wadie@ula.ve
Bibliografia
  • [1] A. Acosta, W. Aziz, J. Matkowski, N. Merentes, Uniformly continuous composition operator in the space of ϕ-Variation functions in the sense of Riesz, Fasc. Math. 43 (2010), 5–11.
  • [2] J. Appell, P.P. Zabrejko, Nonlinear superposition operator, Cambridge University Press, New York, 1990.
  • [3] W. Aziz, H. Leiva, N. Merentes, J.L. Sánchez, Functions of two variables with bounded Φ-variation in the sense of Riesz, J. Anal. Math. (2009), in press; accepted.
  • [4] V.V. Chistyakov, Mappings of generalized variation and composition operators, J. Math. Sci. 110 (2002) 2, 2455–2466.
  • [5] M.A. Krasnosel’skij, Ya.B. Rutickij, Convex functions and Orlicz spaces, Nordhoff, Groningen, 1961.
  • [6] M. Kuczma, An introduction to the theory of functional equations and inequalities, Polish Scientific Editors and Silesian University, Warszawa-Kraków-Katowice, 1985.
  • [7] W.A. Luxemburg, Banach function spaces, Ph.D. thesis, Technische Hogeschool te Delft, Netherlands, 1955.
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  • [9] J. Matkowski, A. Matkowska, N. Merentes, Remark on globally Lipschitzian composition operators, Demonstratio Math. 4 27 (1995) 1, 171–175.
  • [10] J. Matkowski, On Nemytskij operators, Math. Japonica 33 (1988) 1, 81–86.
  • [11] J. Matkowski, Lipschitzian composition operators in some function spaces, Nonlinear Anal. (1997) 3, 719–726.
  • [12] J. Matkowski, N. Merentes, Characterization of globally Lipschitzian composition operators in the Sobolev Space W(n)(p) [a, b], Zeszyty Nauk. Politech. Lódz. Mat. 24 (1993), 90–99.
  • [13] J. Matkowski, J. Miś, On a characterization of Lipschitzian operators of substitution in the space BV (a, b), Math. Nachr. 117 (1984), 155–159.
  • [14] N. Merentes, S. Rivas, El operador de composición en espacios de funciones con algún tipo de variación acotada, IX Escuela Venezolana de Matemáticas, Facultad de Ciencias-ULA, Mérida- Venezuela, 1996.
  • [15] N. Merentes, S. Rivas, On characterization of the Lipschitzian composition operators between spaces of functions of bounded p-variation, Czechoslovak Math. J. 45 (1995) 120, 627–637.
  • [16] H. Nakano, Modulared semi-ordered spaces, Tokyo, 1950.
  • [17] W. Orlicz, A note on modular spaces. I, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 9 (1961), 157–162.
  • [18] F. Riesz, Untersuchugen über Systeme Integrierberer Funktionen, Math. Ann. 69 (1910), 449–497.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGHT-0003-0001
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