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
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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 \[ {\mathbf {K}} = \frac {{{1^{ - 2}} - {3^{ - 2}} + {5^{ - 2}} - {7^{ - 2}} + \cdots }}{{{1^{ - 2}} + {3^{ - 2}} + {5^{ - 2}} + {7^{ - 2}} + \cdots }}.\] This complements the recent result of Burgess Davis that the best constant in Kolmogorov’s inequality is ${{\mathbf {K}}^{ - 1}}$.
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© Copyright 1976
American Mathematical Society