A.E Convergence and 2-Weight Inequalities for Poisson-Laguerre Semigrops

Abstract

We find optimal decay estimates for the Poisson kernels associated with various Laguerre-type operators L. From these, we solve two problems about the Poisson semigroup e-tL. First, we find the largest space of initial data f so that e-tLf(x)→f(x) at a.e.x. Secondly, we characterize the largest class of weights w which admit 2-weight inequalities of the form ‖sup0.