Asympotic bounds for Bombieri's inequality on products of homogeneous polynomials

2024/02/29 by Aldaz, J. M., Render, H.
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2402.19153

Abstract

Let P be a fixed homogeneous polynomial. We present a sharp condition on P guaranteeing the existence of asymptotically larger bounds in Bombieri's inequality, so for every homogeneous polynomial q_m of degree m we have \Vert P q_m\Vert _a≥ C_P m^{l( P) /2}\Vert q_m\Vert _a, where ‖ ⋅ ‖ _a denotes the apolar norm. Explicit estimates for C_P > 0 and l(P) > 0 are given.

Related

• The apolar inner product and a Bombieri type inequality for polynomials
• Some asymptotic estimates on the Von Neumann Inequality for homogeneous polynomials
• A note on the polynomial Bohnenblust-Hille inequality
• A note on the hypercontractivity of the polynomial Bohnenblust--Hille inequality
• Complex polynomial Bohnenblust--Hille inequality with polynomial bounds