Estimates on the norm of polynomials and applications

Abstract

In this paper, equivalence constants between various polynomial norms are calculated. As an application, we also obtain sharp values of the Hardy--Littlewood constants for $2$-homogeneous polynomials on ${\ell }_p^2$ spaces, $2<p\le \infty$ and lower estimates for polynomials of higher degrees.

References in corpus (4)

• The Bohnenblust--Hille inequality for homogeneous polynomials is hypercontractive
• Optimal Hardy-Littlewood type inequalities for polynomials and multilinear operators
• New lower bounds for the constants in the real polynomial Hardy--Littlewood inequality
• Sharp values for the constants in the polynomial Bohnenblust-Hille inequality

Cited by in corpus (1)

• Remarks on the Hardy--Littlewood inequality for $m$-homogeneous polynomials and $m$-linear forms