On multipliers preserving the classes of functions with a given major of the modulus of continuity

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Abstract

A necessary and sufficient condition is obtained for (Cω, Cω) multipliers in the case of a slowly decreasing majorant of the modulus of continuity ω(δ). For the Lipschitz classes this result is equivalent to a theorem of A. Zygmund (J. Math. Mech. 8 (1959), 889–895).

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