On the Inclusion H2 Un. ;H2 n B.and the n Isoperimetric Inequality

Let Un and Bn be the unit polydisc and the unit all in Cn, respectively. We prove that if f is in the Hardy space H2 Un., then f is inH2 n Bn.and that the norm of the inclusion is equal to one. If f depends on one variable only, then the result reduces to an inequality of isoperimetric type due to Carleman ns2.and Burbea n)2..