## Local smoothness of an analytic function compared to the smoothness of its modulus.(English. Russian original)Zbl 1302.30075

St. Petersbg. Math. J. 25, No. 3, 397-420 (2014); translation from Algebra Anal. 25, No. 3, 52-85 (2013).
Summary: Let $$\Phi$$ be a function analytic in the disk and continuous up to the boundary, and let its modulus of continuity satisfy the Hölder condition of order $$\alpha$$, $$0<\alpha <2$$, at a single boundary point. Under standard assumptions on the zeros of $$\Phi$$, this function must be then at least $$\alpha /2$$-Hölder (in a certain integral sense) at the same point. There are generalizations to not necessarily power-type Hölder smoothness.

### MSC:

 30J99 Function theory on the disc

### Keywords:

analytic functions in the disk; Hölder continuity
Full Text:

### References:

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