In this work, we prove that the complement of the Brjuno set \(\mathcal {B}\) has a zero capacity with respect to the kernel \(k^1_\sigma (z,\xi )=\ln ^2{|z-\xi |}\left| \ln {\ln {\left( e+\frac{1}{|z-\xi |}\right) }}\right| ^\sigma \) for any \(\sigma > 2\) . Similarly, the complement of the Perez-Marco set \(\mathcal{P}\mathcal{M}\) has a zero capacity with respect to the kernel \(k^2_\sigma (z,\xi ) = \ln ^{2}{\ln \left( e+\frac{1}{\left| {z - \xi }\right| }\right) }\cdot \ln ^{\sigma }{\ln \ln \left( e^3+\frac{1}{\left| {z - \xi }\right| }\right) }\) for any \(\sigma >2\) .
