Orlicz-Lorentz Spaces and their Composition Operators
DOI:
https://doi.org/10.4067/S0716-09172015000100007Keywords:
Orlicz-Lorentz space.Abstract
In a self-contained presentation, we discuss the Orlicz-Lorentz space. Also the boundedness of composition operators on Orlicz-Lorentz spaces are characterized in this paper.References
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[13] M. M. Rao and Z. D. Ren, Theory of Orlicz spaces, Marcel Dekker Inc., New York, (1993).
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[15] R. K. Singh and J. S. Manhas, Composition operators on Function Spaces, North Holland Math. Stud. Vol. 179, Elsevier Science Publications, Amsterdem, New York, (1993).
[2] Y. A. Abramovich, C. D. Aliprantis, An Invitation to Operator Theory, American Mathematical Society, (2002).
[3] S.C Arora, Gopal Datt and Satish Verma, Multiplication operators on lorentz spaces, Indian Journal of Mathematics, Vol. 48, (3), pp. 317-329, (2006).
[4] A. Axler, Multiplication operators on Bergman space, J. Peine Angew Math., Vol. 33 (6), pp. 26-44, (1982).
[5] Grafakos, Loukas. Classical Fourier Analysis Second Edition, Springer, (2008).
[6] R. E. Castillo, R. León; E. Trousselot. Multiplication operator on L(p, q) spaces, Panamer. Math Journal Vol. 19, No. 1, pp. 37-44, (2009).
[7] Y. Cui, H. Hudzik, Romesh Kumar and L. Maligranda, Composition operators in Orlicz spaces, J. Austral. Math. Soc., Vol. 76 (2), pp. 189-206, (2004).
[8] H. Hudzik, A. Kaminska and M. Mastylo, On the dual of Orlicz Lorentz space, Proc. Amer. Math. Soc., Vol. 130 (6), pp. 1645-1654, (2003).
[9] B. S. Komal and Shally Gupta, Multiplication operators between Orlicz spaces, Integral Equations and Operator Theory. Vol. 41, pp. 324- 330, (2001).
[10] Romesh Kumar, Composition operators on Orlicz spaces, Integral Equations and Operator Theory. Vol. 29, pp. 17-22, (1997).
[11] Rajeev Kumar and Romesh Kumar, Compact composition operators on Lorentz spaces, Math. Vesnik, Vol. 57, pp. 109-112, (2005).
[12] E. Nordgren, Composition operators on Hilbert spaces, Lecture notes in Math., Vol. 693, pp. 37-68, Springer Verlag, New York, (1978).
[13] M. M. Rao and Z. D. Ren, Theory of Orlicz spaces, Marcel Dekker Inc., New York, (1993).
[14] R. K. Singh and A. Kumar, Multiplication and composition operators with closed ranges, Bull. Aust. Math. Soc. Vol. 16, pp. 247-252, (1977).
[15] R. K. Singh and J. S. Manhas, Composition operators on Function Spaces, North Holland Math. Stud. Vol. 179, Elsevier Science Publications, Amsterdem, New York, (1993).
How to Cite
[1]
R. E. Castillo, H. C. Chaparro, and J. C. Ramos Fernández, “Orlicz-Lorentz Spaces and their Composition Operators”, Proyecciones (Antofagasta, On line), vol. 34, no. 1, pp. 85-105, 1.
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