Analyticity of Higher-Order Moduli of Continuity of Real-Analytic Functions - Dovgoshei, A. A.; Potemkina, L. L. (Ukrains’kyi Matematychnyi Zhurnal, 2003)
The Perel’man’s result according to which the first modulus of continuity of any real-analytic function f is a function analytic in a certain neighborhood of the origin is generalized to the case of arbitrary moduli of continuity of higher order.