This is an announcement for the paper "Non-linear Plank Problems and polynomial inequalities" by Daniel Carando, Damian Pinasco and Jorge Tomas Rodriguez.

Abstract: In this article we study plank type problems for polynomials on a Banach space $X$. Our aim is to find sufficient conditions on the positive real numbers $a_1, \ldots, a_n,$ such that for continuous polynomials $P_1,\ldots,P_n:X\rightarrow \mathbb C$ of degrees $k_1,\ldots,k_n$, there exists a norm one element $\textbf{z}\in X$ for which $|P_i(\textbf{z})| \ge a_i^{k_i}$ for $i=1,\ldots,n.$ In order to do this, we prove some new inequalities for the norm of the product of polynomials, which are of an independent interest.

Archive classification: math.FA

Remarks: 18 pages

Submitted from: jtrodrig@dm.uba.ar

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1507.02316

or

http://arXiv.org/abs/1507.02316