Various upper bounds for the L2-norm of theWick 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.

Holder type inequalities for norms of Wick products

LANCONELLI, ALBERTO;
2008

Abstract

Various upper bounds for the L2-norm of theWick 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11586/74170
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