Sharp inequalities over the unit polydisc

Motivated by some results due to Burbea we prove that if a certain sharp integral inequality holds for functions in the unit polydisc which belong to concrete Hardy spaces, then it also holds, in an appropriate form, in the case of functions from arbitrary Hardy spaces. We also examine the equality case. We present an application of this main result to a Burbea inequality which includes an isoperimetric type inequality as a special case.