Abstract. Some reverse Hölder type inequalities yielding for monotone or quasimonotone functions of one variable have recently been obtained and applied (see e.g. [2-5], [14]). In this paper we prove a sharp multidimensional integral inequality of this type. It is pointed out that this inequality may be regarded as a unification and extension of many inequalities of this type including some recent results in [1] and [11].

AMS Subject Classification (1991): 26D15, 26D07, 26D20

Keyword(s): Inequalities, integral inequalities, reverse Hölder inequalities, monotone functions, several variables, best constants

Received October 10, 1995 and in revised form April 10, 1996. (Registered under 6124/2009.)