Exposed points and extremal problems in H1 on a bidisc

An essential bounded function ? gives a continuous linear functional on the Hardy space H¹ on the bitorus. In this paper, we consider extremal problems on H¹ when ? is a rational function, ? is a product of one variable functions or ? = |f|/f for some outer function f in H¹ such that f(z, w) has a good property with respect to w for a.e. z. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)