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

Text In this note, among other results, we find the optimal constants of the generalized Bohnenblust–Hille inequality for m -linear forms over R and with multiple exponents ( 1 , 2 , … , 2 ) , sometimes called mixed ( ℓ 1 , ℓ 2 ) -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 . Video For a video summary of this paper, please visit https://youtu.be/KnKtjbvsbW0 . [ABSTRACT FROM AUTHOR]