The authors give an upper bound of the essential norm of a composition operator on H2(Bn),which involves the counting function in the higher dimensional value distribution theory defined by S.S.Chern.A criterion is also given to assure that the composition operator on H2(Bn) is bounded or compact.
In this paper, we define the generalized counting functions in the higher dimensional case and give an upper bound of the essential norms of composition operators between the weighted Bergman spaces on the unit ball in terms of these counting functions. The sufficient condition for such operators to be bounded or compact is also given.
The authors give an upper bound of the essential norms of composition opera- tors between Hardy spaces of the unit ball in terms of the counting function in the higher dimensional value distribution theory defined by Professor S. S. Chern. The sufficient condition for such operators to be bounded or compact is also given.
