IJPAM: Volume 78, No. 2 (2012)
WEIGHTED BERGMAN SPACES OF THE UNIT BALL
Department of Mathematical Sciences
Montana Tech of The University of Montana
1300, West Park Street, Butte, Montana, 59701, USA
Department of Mathematics
Central Michigan University
Washington Street, Mount Pleasant, Michigan, 48859, USA
Abstract. Suppose is an analytic self map of and is analytic on . Then a weighted composition operator induced by with weight is given by for in and f analytic on . Given we characterize boundedness and compactness of , where and . We also characterize the Schatten -class weighted composition operators for and .
Received: December 27, 2011
AMS Subject Classification: 47B38, 32A35, 32A36
Key Words and Phrases: weighted composition operators, Bergman spaces, Toeplitz operators, the Berezin transform, Schatten -class, unit ball of
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395