WEIGHTED COMPOSITION OPERATORS BETWEEN BERGMAN-TYPE SPACES

Title & Authors
WEIGHTED COMPOSITION OPERATORS BETWEEN BERGMAN-TYPE SPACES
Sharma, Ajay K.; Sharma, Som Datt;

Abstract
In this paper, we characterize the boundedness and compactness of weighted composition operators ${\psi}C_{\varphi}f Keywords weighted Bergman spaces;growth spaces;weighted composition operator;composition operator;multiplication operator; Language English Cited by 1. On a product-type operator from Bloch spaces to weighted-type spaces on the unit ball, Applied Mathematics and Computation, 2011, 217, 12, 5930 2. Composition operators from the space of Cauchy transforms to Bloch and the little Bloch-type spaces on the unit disk, Applied Mathematics and Computation, 2011, 217, 24, 10187 3. Weighted Composition Operators from Weighted Bergman Spaces to Weighted-Type Spaces on the Upper Half-Plane, Abstract and Applied Analysis, 2011, 2011, 1 4. Weighted composition operators between weighted Bergman spaces, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, 2009, 103, 1, 11 5. Weighted Iterated Radial Composition Operators between Some Spaces of Holomorphic Functions on the Unit Ball, Abstract and Applied Analysis, 2010, 2010, 1 References 1. K. R. M. Attele, Multipliers of composition operators, Tokyo J. Math. 15 (1992), 185-198 2. M. D. Contreras and A. G. Hernandcz-Diaz, Weighted composition operators on Hardy spaces, J. Math. Anal. Appl. 263 (2001), 224-233 3. M. D. Contreras and A. G. Hernandcz-Diaz, Weighted composition operators on spaces of functions with derivatiae in a Hardy space, J. Operator Theory 52 (2004), 173-184 4. C. C. Cowen and B. D. MacCluer, Composition operators on spaces of analytic functions, CRC Press Boca Raton, New York, 1995 5. Z. Cuckovic and R. Zhao, Weighted composition operators on the Bergman space, J. London Math. Soc. 70 (2004), 499-51l 6. F. Forelli, The isometries of$H^P$spaces, Canad. J Math. 16 (1964), 721-728 7. H. Hedenmalm, B. Korenblum and K. Zhu, Theory of Bergman spaces, Springer, New York, Berlin, etc. 2000 8. K. Hoffman, Banach spaces of analytic functions, Dover Publications, Inc., 1988 9. H. Kamowitz, Compact operators of the form$uC_{\varphi}$, Pacific J. Math. 80 (1979), 205-211 10. J. E. Littlewood, On inequalities in the theory of functions, Proc. London Math. Soc. 23 (1925) 11. B. D. MacCluer and J. H. Shapiro, Angular derivatives and compact composition operators on Hardy and Bergman spaces, Can. J. Math. 38 (1986), 878-906 12. V. Matache, Compact composition operators on Hardy spaces of a half-plane, Proc. Amer. Math. Soc. 127 (1999), 1483-1491 13. G. Mirzakarimi and K. Seddighi, Weighted composition operators on Bergman and Dirichlet spaces, Georgian. Math. J. 4 (1997), 373-383 14. H. J. Schwartz, Composition operators on$H^p$, Thesis, University of Toledo, 1969 15. J. H. Shapiro and P. D. Taylor, Compact, nuclear and Hilbert-Schmidt composition operators on$H^2\$, Indiana Univ. Math J. 23 (1973), 471-496

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