Abstract. In this article we examine Dirichlet type spaces in the unit polydisc, and multipliers between these spaces. These results extend the corresponding work of G. D. Taylor in the unit disc. In addition, we consider functions on the polydisc whose restrictions to lower dimensional polydiscs lie in the corresponding Dirichet type spaces. We see that such functions need not be in the Dirichlet type space of the whole polydisc. Similar observations are made regarding multipliers.

AMS Subject Classification (1991): 46E22, 46E20, 47B32

Keyword(s): Dirichlet type spaces, multipliers

Received January 21, 2005, and in revised form October 28, 2005. (Registered under 5917/2009.)