In mathematical analysis, Littlewood's 4/3 inequality, named after John Edensor Littlewood, is an inequality that holds for every complex-valued bilinear form defined on , the Banach space of scalar sequences that converge to zero.
Precisely, let or be a bilinear form. Then the following holds:
where
The exponent 4/3 is optimal, i.e., cannot be improved by a smaller exponent. It is also known that for real scalars the aforementioned constant is sharp.
BohnenblustâÂÂHille inequality is a multilinear extension of Littlewood's inequality that states that for all -linear mapping the following holds: