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A HÖLDER INEQUALITY FOR NORMS OF POISSONIAN WICK PRODUCTS

ALBERTO LANCONELLI

Dipartimento di Matematica, Universita' degli Studi di Bari, Via E. Orabona, 4, 70125 Bari, Italia

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and

AUREL I. STAN

Department of Mathematics, Ohio State University at Marion, 1465 Mount Vernon Avenue, Marion, OH 43302, U. S. A.

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https://doi.org/10.1142/S0219025713500227Cited by:5 (Source: Crossref)

Abstract

An understanding of the second quantization operator of a constant times the identity operator and the Poissonian Wick product, without using the orthogonal Charlier polynomials, is presented first. We use both understanding, with and without the Charlier polynomials, to prove some inequalities about the norms of Poissonian Wick products. These inequalities are the best ones in the case of L¹, L², and L^∞ norms. We close the paper with some probabilistic interpretations of the Poissonian Wick product.

Keywords:

AMSC: 60H40, 60H10, 46B70

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