Abstract:
The problem of finding the exact upper bound of the values of the modules of continuity of conjugate functions with fixed step value $h$ is studied. The exact upper bound is taken from a set of $2\pi$-periodic functions that satisfy the Lipschitz condition of first order with a given Lipschitz constant. Åxtreme asymptotics in this problem were found with accuracy up to $O(h^3)$ for $h\rightarrow 0+$. The margin of error is estimated clearly.
Key words:conjugate function, modulus of continuity, Lipschitz condition.
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