A Note on Multiplication Operators Between Orlicz Spaces

Heera Saini1 and Isha Gupta2


1Department of Mathematics, G.C.E.T, Jammu, Jammu and Kashmir, India.
2Department of Statistics, University of Jammu, Jammu, Jammu and Kashmir, India.

Abstract: In this paper, we study the boundedness of multiplication operators between any two Orlicz spaces.
Keywords: Multiplication operators, Boundedness, Orlicz spaces, Musielak-Orlicz spaces.


Cite this article as: Heera Saini and Isha Gupta, A Note on Multiplication Operators Between Orlicz Spaces, Int. J. Math. And Appl., vol. 9, no. 2, 2021, pp. 1-4.

References
  1. M. B. Abrahamese, Multiplication operators, Lecture Notes in Math., 693(1978), 17-36.
  2. S. C. Arora, G. Datt and S. Verma, Multiplication operators on Lorentz spaces, Indian Journal of Math., 48(3)(2006), 317-329.
  3. S. Chen, Geometry of Orlicz spaces, Dissertations Math., 356(1996), 1-204.
  4. L. Drewnowski and W. Orlicz, A note on modular spaces XI, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys., 16(1968), 877-882.
  5. S. Gupta and B. S. Komal, Multiplication operators between Orlicz spaces, Integral Equations and Operator Theory, 41(2001), 324-330.
  6. Y. Cui , H.~Hudzik, R. Kumar and L. Maligranda, Composition operators in Orlicz spaces, J. Aust. Math. Soc., 76(2004), 189-206.
  7. H. Hudzik and L.mMaligranda, Amenya norm equals Orlicz norm in general, Indag. Math. N. S., 11(2000), 573-585.
  8. B. S. Komal and S. Gupta, Multiplication operator between Orlicz spaces, Integr. Equ. Oper. Theory, 41(2001), 324-330.
  9. M. A. Krasnoselkii and Ya. B. Rutickii, Convex functions and Orlicz spaces, Noordhoff, Graningen, (1961).
  10. R. Kumar, Composition operators on Orlicz spaces, Integral Equations and Operator Theory, 29(1997), 17-22.
  11. L. Maligranda, Orlicz Spaces and Interpolation, Seminars in Math. 5, Univ. Estadual de Campinas, Campinas SP, Brazil, (1989).
  12. L. Maligranda, Some remarks on Orlicz's interpolation theorem, Studia Math., 95(1989), 43-58.
  13. J. Musilek, Orlicz spaces and modular spaces, Lecture Notes in Math. 1034, Springer-Verlag, Berlin-New York, (1983).
  14. M. M. Rao and Z. D. Ren, Theory of Orlicz spaces, Marcel Dekker, New York, (1991).
  15. M. M. Rao and Z. D. Ren, Applications of Orlicz spaces, Marcel Dekker, New York, (2002).
  16. H. Takagi and K. Yokouchi, Multiplication and composition operators between two $L^p-$spaces, in: Function Spaces (Edwardsville, IL 1998), Contemp. Math. 232, Amer. Math. Soc., Providence, RI (1999), 321-338.

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