Journal of Applied Mathematics and Stochastic Analysis
Volume 2008 (2008), Article ID 254897, 22 pages
Hölder-Type Inequalities for Norms of Wick Products
1Dipartimento di Matematica, Università di Bari, Campus Universitario, Via E. Orabona 4, 70125 Bari, Italy
2Department of Mathematics, Ohio State University at Marion, 1465 Mount Vernon Avenue, Marion, OH 43302, USA
Received 3 November 2007; Revised 21 January 2008; Accepted 26 February 2008
Academic Editor: Enzo Orsingher
Copyright © 2008 Alberto Lanconelli and Aurel I. Stan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Various upper bounds for the -norm of the Wick product of two
measurable functions of a random variable , 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.