Lower bounds for norms of products of polynomials on L_p spaces

CARANDO DANIEL; PINASCO DAMIAN; RODRÍGUEZ, JORGE TOMÁS

STUDIA MATHEMATICA

POLISH ACAD SCIENCES INST MATHEMATICS

Lugar: VARSOVIA; Año: 2013 vol. 214 p. 157 - 166

0039-3223

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 infinitedimensional settings). The result also holds for the Schatten classes $Sp$. For $p > 2$ we present some estimates on the constants involved.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 infinitedimensional settings). The result also holds for the Schatten classes $Sp$. For $p > 2$ we present some estimates on the constants involved.