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Apr 1 at 12:30 comment added Akira Thank you so much for your answer! Could you have a look at this closely related question? Basically, I asked if there is a sequence $(f_n) \subset \mathcal D_1$ such that $\lim_n \frac{[\rho * f_n]_\alpha}{\|\rho * f_n\|_\infty} = \infty$.
Apr 1 at 12:26 vote accept Akira
Apr 1 at 12:17 history answered Pietro Majer CC BY-SA 4.0