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Since I finished my doctoral dissertation entitle "Singular Integrals with respect to the Gaussian measure", chaired by Professor Eugene Fabes at the University of Minnesota, I have been working in what we call Gaussian harmonic analysis that is to say the study the notions of the classical Harmonic Analysis (with respect to the Lebesgue measure) like Hardy-Littlewood maximal functions, singular integrals, multipliers, Littlewood-Paley theory, etc, but with respect to the Gaussian measure. As a natural development of the study of the Hermite polynomials, which plays an important role in the Gaussian harmonic analysis and became interested in the theory of orthogonal polynomials and the harmonic analysis associated with them. Besides my interest in harmonic analysis in general and in particular harmonic analysis of orthogonal polynomial I am also interested in wavelets as well as probability theory, especially in martingale theory and its connection to analysis, and stochastic Integrals