About projections of logarithmic Sobolev inequalities

We derive bounds for the logarithmic Sobolev constant associated to some finite type Fleming-Viot operators different from those recently obtained by Stannat. We will verify that on large subdomains of the space of underlying parameters, our estimates axe of the right order, nevertheless, the result of Stannat remains better for some small values. Our approach is based on an uplifting of the problem to gamma distribution product spares, leading us to evaluate the logarithmic Sobolev constant corresponding to Laguerre operators via Hardy's inequalities techniques.