Orlicz-Lorentz Spaces and their Composition Operators

• Castillo, René Erlin ; Chaparro, Héctor Camilo ^[1] ; Ramos Fernández, Julio César ^[2]
  1. [1] Universidad Nacional de Colombia

     Universidad Nacional de Colombia

     Colombia

     
  2. [2] Universidad de Oriente

     Universidad de Oriente

     Venezuela

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 34, Nº. 1, 2015, págs. 85-105
• Idioma: inglés
• DOI: 10.4067/S0716-09172015000100007
• Enlaces
  • Texto completo
• Resumen

  • 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.

• Referencias bibliográficas
  • Citas [1] M. B. Abrahamese, Multiplication operators, Lecture notes in Math., Vol. 693, pp. 17-36, Springer Verlag, New York, (1978).
  • [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,...
  • [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,...
  • [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-...
  • [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,...