Extremal problems in H¹ for continuous kernels on a bidisc

Abstract

Let B _φ be a bounded linear functional on the Hardy space H ¹ on the bidisc, defined by an essentially bounded function φ. When φ is a continuous function, we study the solution set S _φ of an extremal problem, that is, S _φ = { f ∈ H ¹: B _φ(f) = ‖B _φ‖ and ‖ f ‖₁ = 1}.

Keywords:

• Hardy space
• continuous function
• exposed point
• linear functional
• extremal problem

AMS Subject Classifications::

• 32A35
• 42B30

Acknowledgements

This research is partially supported by Grant-in-Aid Research No.20540148.