New lower bounds for the constants in the real polynomial Hardy--Littlewood inequality

Abstract

In this short note we obtain new lower bounds for the constants of the real Hardy--Littlewood inequality for $m$-linear forms on ${\ell }_p^2$ spaces when $p=2m$ and for certain values of $m$. The real and complex cases for the general case ${\ell }_p^n$ were recently investigated by G. Araujo et al. When $n=2$ our results improve the best known estimates for these constants.

References in corpus (1)

• Sharp values for the constants in the polynomial Bohnenblust-Hille inequality

Cited by in corpus (1)

• Estimates on the norm of polynomials and applications