Local smoothness of the conjugate functions
type: Item
instance of: scholarly article
zbMATH Open document ID: 1271.42009
author: M. I. Dyachenko
publication date: 2012-09-07T00:00:00Z
Mathematics Subject Classification ID: 42A50
zbMATH DE Number: 6079028
zbMATH Keywords: conjugate functions
zbMATH Keywords: local smoothness
MaRDI profile type: Publication
title: Local smoothness of the conjugate functions
published in: Eurasian Mathematical Journal
review text: 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.
reviewed by: Petr Gurka
description: scientific article; zbMATH DE number 6079028