The class of Meixner random variables can be described in terms of a Lie Algebra structure generated by their quantum operators. This Lie Algebra structure is useful in computing first the kernels that give the second quantization operators, and then the Wick products generated by these random variables. We restrict our attention to three of the most important types of Meixner random variables: Gaussian, Poisson, and Gamma, and present some H ̈older inequalities for the norms of the Wick products generated by them. We show that these inequalities are related to sharp inequalities from classic Harmonic Analysis concerning the norms of some convolution-type products.