WEIGHTED COMPOSITION OPERATORS ON LORENTZ SPACES

Title & Authors
WEIGHTED COMPOSITION OPERATORS ON LORENTZ SPACES
Arora, Subhash Chander; Datt, Gopal; Verma, Satish;

Abstract
In this paper we characterize the boundedness, compactness and closedness of the range of the weighted composition operators on Lorentz spaces L(p,q), $1 Keywords distribution function;Lorentz space;multiplication operator;non-increasing rearrangement;weighted composition operator; Language English Cited by 1. Injective composition operators on Lorentz–Bochner spaces, Demonstratio Mathematica, 2013, 46, 4 References 1. S. C. Arora, G. Datt, and S. Verma, Multiplication operators on Lorentz spaces, Indian J. Math. 48 (2006), no. 3, 317-329 2. C. Bennett and R. Sharpley, Interpolation of operators, Pure and Applied Mathematics, 129. Academic Press, Inc., Boston, MA, 1988 3. J. T. Chan, A note on compact weighted composition operators on$L^p$( ), Acta Sci. Math. (Szeged) 56 (1992), no. 1-2, 165-168 4. H. Hudzik, Rajeev Kumar, and Romesh Kumar, Matrix multiplication operators on Banach function spaces, Proc. Indian Acad. Sci. Math. Sci. 116 (2006), no. 1, 71-81 5. R. A. Hunt, On L(p, q) spaces, Enseignement Math. (2) 12 (1966), 249-276 6. M. R. Jabbarzadeh and E. Pourreza, A note on weighted composition operators on$L^p$-spaces, Bull. Iranian Math. Soc. 29 (2003), no. 1, 47-54 7. M. R. Jabbarzadeh, Weighted composition operators between$L^p$-spaces, Bull. Korean Math. Soc. 42 (2005), no. 2, 369-378 8. B. S. Komal and Shally Gupta, Composition operators on Orlicz spaces, Indian J. Pure Appl. Math. 32 (2001), no. 7, 1117-1122 9. R. Kumar and R. Kumar, Composition operators on Banach function spaces, Proc. Amer. Math. Soc. 133 (2005), no. 7, 2109-2118 10. R. Kumar and R. Kumar, Compact composition operators on Lorentz spaces, Mat. Vesnik 57 (2005), no. 3-4, 109-112 11. G. G. Lorentz, Some new functional spaces, Ann. of Math. (2) 51 (1950), 37-55 12. G. G. Lorentz, On the theory of spaces$\wedge\$, Pacific J. Math. 1 (1951), 411-429

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