Lower bounds for norms of products of polynomials on $L_p$ spaces
Volume 214 / 2013
Studia Mathematica 214 (2013), 157-166
MSC: 32A22, 51M16, 52A40, 46G25.
DOI: 10.4064/sm214-2-4
Abstract
For $1 < p < 2$ we obtain sharp lower bounds for the uniform norm of products of homogeneous polynomials on $L_p(\mu )$, whenever the number of factors is no greater than the dimension of these Banach spaces (a condition readily satisfied in infinite-dimensional settings). The result also holds for the Schatten classes $\mathcal S_p$. For $p>2$ we present some estimates on the constants involved.
