Abstract
Suppose Φ is an analytic self map of B n and φ is analytic on B n. Then a weighted composition operator induced by Φ with weight φ is given by (W φ,ρf) (z) = φ(z)f(Φ(z)) for z in B n and f analytic on B n. Given W φ,Φ: A p α(B n) → A q βj(B n) we characterize boundedness and compactness of W φ,ρ, where 0 p,q < ∞ and -1 < α, β < ∞. We also characterize the Schatten p-class weighted composition operators S p (A 2 α(B n)) for 0 < p < ∞ and -1< α < ∞.
Original language | English |
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Pages (from-to) | 161-183 |
Number of pages | 23 |
Journal | International Journal of Pure and Applied Mathematics |
Volume | 78 |
Issue number | 2 |
State | Published - 2012 |
Keywords
- Bergman spaces
- Schatten p-class
- The Berezin transform
- Toeplitz operators
- Unit ball of ℂ
- Weighted composition operators