1 results
ESSENTIAL NORM OF EXTENDED CESÀRO OPERATORS FROM ONE BERGMAN SPACE TO ANOTHER
- Part of
-
- Journal:
- Bulletin of the Australian Mathematical Society / Volume 85 / Issue 2 / April 2012
- Published online by Cambridge University Press:
- 12 December 2011, pp. 307-314
- Print publication:
- April 2012
-
- Article
-
- You have access
- Export citation
-
Let Ap(φ) be the pth Bergman space consisting of all holomorphic functions f on the unit ball B of ℂn for which
, where φ is a given normal weight. Let Tg be the extended Cesàro operator with holomorphic symbol g. The essential norm of Tg as an operator from Ap (φ) to Aq (φ) is denoted by 
. In this paper it is proved that, for p≤q, 
with 1/k=(1/p)−(1/q) , where ℜg(z) is the radial derivative of g; and for p>q, 
with 1/s=(1/q)−(1/p) .
, where φ is a given normal weight. Let 
. In this paper it is proved that, for 
