2016/04/20 by Mariana Maia, Maia, Mariana, Joedson Santos +1
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1604.06142
openalex publication_date 2016/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is well-known that the optimal constant of the bilinear Bohnenblust--Hille inequality (i.e., Littlewood's 4/3 inequality) is obtained by interpolating the bilinear mixed ( ℓ 1,ℓ2) -Littlewood inequalities. We remark that this cannot be extended to the 3-linear case and, in the opposite direction, we show that the asymptotic growth of the constants of the m-linear Bohnenblust--Hille inequality is the same of the constants of the mixed ( ℓ (2m+2)/(m+2),ℓ 2) -Littlewood inequality. This means that, contrary to what the previous works seem to suggest, interpolation does not play a crucial role in the search of the exact asymptotic growth of the constants of the Bohnenblust--Hille inequality. In the final section we use mixed Littlewood type inequalities to obtain the optimal cotype constants of certain sequence spaces.