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Lower bounds for norms of products of polynomials on $L_{p}$ spaces

Daniel Carando; Damián Pinasco; Jorge Tomás Rodríguez — 2013

Studia Mathematica

For 1 < p < 2 we obtain sharp lower bounds for the uniform norm of products of homogeneous polynomials on $L_{p} (μ)$ , 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 $_{p}$ . For p > 2 we present some estimates on the constants involved.

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Lower bounds for norms of products of polynomials on L p spaces

Lower bounds for norms of products of polynomials on $L_{p}$ spaces