in this paper we obtain lower and upper estimates for the essential norms of generalized composition operators from weighted dirichlet spaces or bloch type spaces to $q_k$ type spaces.

Since the seminal work of Lindblom (1963) a wealth of studies have investigated undershoot and the factors governing its occurrence and variability. However, although sex-specific differences in reduction patterns have been found in adults (Byrd 1994; Whiteside 1996), as well as in children (McCormack & Knighton 1996), possible sex-specific differences in formant transitions and in particular u...