Local smoothness of the conjugate functions
The aim of this paper is to study the local behaviour in a particular point of the conjugate function \(\widetilde f\), NEWLINE\[NEWLINE \widetilde f(x)=-\frac1\pi\int_0^\pi\frac{f(x+t)-f(x-t)}{2\tan(t/2)}\, \text{d}t, NEWLINE\]NEWLINE if the global smoothness as well as the behaviour at this point of the original function \(f\) are known. The author obtains several sharp results concerning this problem and solves some related problems.
scientific article; zbMATH DE number 6079028