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http://dx.doi.org/10.4134/BKMS.2007.44.4.701

WEIGHTED COMPOSITION OPERATORS ON LORENTZ SPACES  

Arora, Subhash Chander (DEPARTMENT OF MATHEMATICS UNIVERSITY OF DELHI)
Datt, Gopal (DEPARTMENT OF MATHEMATICS PGDAV COLLEGE UNIVERSITY OF DELHI)
Verma, Satish (DEPARTMENT OF MATHEMATICS SGTB KHALSA COLLEGE UNIVERSITY OF DELHI)
Publication Information
Bulletin of the Korean Mathematical Society / v.44, no.4, 2007 , pp. 701-708 More about this Journal
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;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
Times Cited By Web Of Science : 1  (Related Records In Web of Science)
Times Cited By SCOPUS : 3
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1 S. C. Arora, G. Datt, and S. Verma, Multiplication operators on Lorentz spaces, Indian J. Math. 48 (2006), no. 3, 317-329
2 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   DOI
3 C. Bennett and R. Sharpley, Interpolation of operators, Pure and Applied Mathematics, 129. Academic Press, Inc., Boston, MA, 1988
4 J. T. Chan, A note on compact weighted composition operators on $L^p$( ), Acta Sci. Math. (Szeged) 56 (1992), no. 1-2, 165-168
5 R. A. Hunt, On L(p, q) spaces, Enseignement Math. (2) 12 (1966), 249-276
6 R. Kumar and R. Kumar, Compact composition operators on Lorentz spaces, Mat. Vesnik 57 (2005), no. 3-4, 109-112
7 G. G. Lorentz, Some new functional spaces, Ann. of Math. (2) 51 (1950), 37-55   DOI
8 G. G. Lorentz, On the theory of spaces $\wedge$, Pacific J. Math. 1 (1951), 411-429   DOI
9 R. K. Singh and J. S. Manhas, Composition operators on function spaces, North-Holland Mathematics Studies, 179. North-Holland Publishing Co., Amsterdam, 1993
10 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
11 M. R. Jabbarzadeh, Weighted composition operators between $L^p$-spaces, Bull. Korean Math. Soc. 42 (2005), no. 2, 369-378   과학기술학회마을   DOI   ScienceOn
12 B. S. Komal and Shally Gupta, Composition operators on Orlicz spaces, Indian J. Pure Appl. Math. 32 (2001), no. 7, 1117-1122
13 R. Kumar and R. Kumar, Composition operators on Banach function spaces, Proc. Amer. Math. Soc. 133 (2005), no. 7, 2109-2118   DOI   ScienceOn
14 H. Takagi, Fredholm weighted composition operators, Integral Equations Operator Theory 16 (1993), no. 2, 267-276   DOI
15 E. M. Stein and G. Weiss, Introduction to Fourier analysis on Euclidean spaces, Prince- ton Mathematical Series, No. 32. Princeton University Press, Princeton, N.J., 1971