**2.1 The case** *ν* ¼ **1**

Let the complex unit disk endowed with its Lebesgue measure *μ* and let ∂ID its boundary denote by *L*<sup>2</sup> ð Þ the space of complex-valued measurable functions on with finite norm

$$\left||\boldsymbol{f}\right|| = \int\_{\mathcal{D}} \left|\boldsymbol{f}(\boldsymbol{\xi})\right|^{2} d\mu(\boldsymbol{\xi}).\tag{8}$$

The Logarithmic Potential operator L : *L*<sup>2</sup> ð Þ! *<sup>L</sup>*<sup>2</sup> ð Þ is defined by

$$
\mathcal{L}[f](\mathbf{z}) = \int\_{\rm ID} f(\xi) \log \left( \frac{\mathbf{1}}{|\xi - \mathbf{z}|} \right) d\mu(\xi). \tag{9}
$$
