Abstract
We construct some counterexamples to the statements [1, 2.3.6] claiming maximal inequalities for the spaces \( B_{p,q}^{s}(^{n}) \) and \( F_{p,q}^{s}(^{n}) \) and propose a condition for these inequalities to hold. We consider some weighted inequality on a bounded interval \( I \) of the real axis that involves \( f\in C_{0}^{\infty}(I) \) and the derivative of \( f \).
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Funding
The author was partially supported by the Russian Foundation for Basic Research (Grant 19–01–00223).
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Prokhorov, D.V. On Maximal Inequalities. Sib Math J 61, 1120–1131 (2020). https://doi.org/10.1134/S0037446620060129
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DOI: https://doi.org/10.1134/S0037446620060129