Hi,

Let $v(z)$ be a 2x2 matrix depending on a complex variable z, defined on an oriented contour $\Sigma$ in the complex plane. Can anyone tell me the meaning of the notation:

$$||v||_{L^{2}(\Sigma)}$$

As far as I can tell from the author, this quantity is intended to be a norm of some description and so should be a positive real number. I had a guess that it might mean "add the maximum of row 1 to the maximum of row 2, then integrate the absolute value squared over $\Sigma$ and finally take the square root".

Is there anyone who's seen this notation before who can confirm/deny my guess? The context of this notation is related to harmonic analysis and singular integral operators.