Norms of Hankel operators on a bidisc

Abstract

In the Hardy space on the bidisc T 2 {T^2} , if ϕ \phi is a bounded function in the Lebesgue space and if its Fourier series vanishes on half of Z 2 {{\mathbf {Z}}^2} , then the norm of the Hankel operator H ϕ {H_\phi } is equal to the quotient norm of ϕ \phi by the Hardy space H ∞ ( T 2 ) {H^\infty }({T^2}) .