A Hölder-Type Inequality for the <i>C</i>0 Distance and Anosov–Katok Pseudo-Rotations

We prove a H\"older-type inequality for Hamiltonian diffeomorphisms relating the $C^0$ norm, norm of derivative, and Hofer/spectral norm. obtain as consequence that sufficiently fast convergence in metric forces convergence. The second theme our paper is study pseudo-rotations arise from Anosov-Katok method. As an application inequality, we rigidity result such pseudo-rotations.