On the Exponential Integrability of Conjugate Functions

被引：0
作者：
H. Gissy
S. Miihkinen
J. A. Virtanen
机构：
[1] University of Reading,Department of Mathematics
[2] Karlstad University,Department of Mathematics and Computer Science
[3] University of Helsinki,Department of Mathematics
来源：
Journal of Fourier Analysis and Applications | 2021年 / 27卷
关键词：
Exponential integrability; Conjugate function; Hilbert transform; Outer functions; 42A50;
D O I：
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摘要：
We relate the exponential integrability of the conjugate function f~\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\tilde{f}}$$\end{document} to the size of the gap in the essential range of f. Our main result complements a related theorem of Zygmund.
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