BLOCH CONSTANTS OF BOUNDED SYMMETRICAL DOMAINS

Let D-1 and D-2 be two irreducible bounded symmetric domains in the co mplex spaces V-1 and V-2 respectively. Let E be the Euclidean metric o n V-2 and h the Bergman metric on V-1. The Bloch constant b(D-1, D-2) is defined to be the supremum of E(f'(z)x, f'(z)x)(1/2)/h(z)(x, x)(1/2 ), taken over all the holomorphic functions f : D-1 --> D-2 and z is a n element of D-1, and nonzero vectors x is an element of V-1. We find the constants for all the irreducible bounded symmetric domains D-1 an d D-2. As a special case we answer an open question of Cohen and Colon na.