Optimality of CKP-inequality in the critical case

Gao, Fuchang

doi:10.1090/S0002-9939-2013-11825-3

Optimality of CKP-inequality in the critical case
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Proc. Amer. Math. Soc. 142 (2014), 909-914 Request permission

Abstract:

It is proved that the CKP inequality \[ \sqrt {\log N(\textrm {cov}(T),2\varepsilon )} \preceq \frac 1\varepsilon \int _{\varepsilon /2}^\infty \sqrt {\log N(T,r)} dr\] is optimal in the critical case $\log N(T,\varepsilon )=O(\varepsilon ^{-2}|\log \varepsilon |^{-2})$ as $\varepsilon \to 0^+$.

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