Essential norms of weighted composition operators induced by automorphisms of the ball

Let H(t )be the Hilbert spaces of holomorphic functions over the open unit ball B-N with reproducing kernels K-w(z) = (1 - (z, w))(-t), where t > N. This paper give estimates for the norms and essential norms of weighted composition operators induced by members in Aut(BN) on the Hilbert spaces H-t. As applications, the boundedness and compactness of these weighted composition operators are characterized. Moreover, this paper gives estimates of the spectral radius and essential spectral radius of the above weighted composition operators.