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We prove that if d is an integer number bigger than 1 and f_1,...,f_d arecommuting circle diffeomorphisms respectively of class C^(1+\tau_k), where\tau_1 + ... + \tau_k > 1, then these maps are simultaneously conjugate torotations provided that their rotation numbers are independent over therationals.

A Denjoy Theorem for commuting circle diffeomorphisms with mixed Holder derivatives