Hölder-type inequalities for norms of Wick products (Q936988)

Summary: Various upper bounds for the \(L^{2}\)-norm of the Wick product of two measurable functions of a random variable \(X\), having finite moments of any order, together with a universal minimal condition, are proven. The inequalities involve the second quantization operator of a constant times the identity operator. Some conditions ensuring that the constants involved in the second quantization operators are optimal, and interesting examples satisfying these conditions are also included.