Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A best constant for Zygmund's conjugate function inequality


Author: Colin Bennett
Journal: Proc. Amer. Math. Soc. 56 (1976), 256-260
MSC: Primary 42A40
DOI: https://doi.org/10.1090/S0002-9939-1976-0402393-4
MathSciNet review: 0402393
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: When the space $ L{\log ^ + }L$ is given the Hardy-Littlewood norm the best constant in the corresponding version of Zygmund's conjugate function inequality is shown to be

$\displaystyle {\mathbf{K}} = \frac{{{1^{ - 2}} - {3^{ - 2}} + {5^{ - 2}} - {7^{ - 2}} + \cdots }}{{{1^{ - 2}} + {3^{ - 2}} + {5^{ - 2}} + {7^{ - 2}} + \cdots }}.$

This complements the recent result of Burgess Davis that the best constant in Kolmogorov's inequality is $ {{\mathbf{K}}^{ - 1}}$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 42A40

Retrieve articles in all journals with MSC: 42A40


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0402393-4
Article copyright: © Copyright 1976 American Mathematical Society