The optimal constants of the mixed (ℓ1,ℓ2)-Littlewood inequality

TextIn this note, among other results, we find the optimal constants of the generalized Bohnenblust–Hille inequality for m  -linear forms over RR and with multiple exponents (1,2,…,2)(1,2,…,2), sometimes called mixed (ℓ1,ℓ2)(ℓ1,ℓ2)-Littlewood inequality. We show that these optimal constants are precisely (2)m−1 and this is somewhat surprising since a series of recent papers have shown that similar constants have a sublinear growth. This result answers a question raised by Albuquerque et al. in a paper published in 2014 in the Journal of Functional Analysis.VideoFor a video summary of this paper, please visit https://youtu.be/KnKtjbvsbW0.