A.e. convergence and 2-weight inequalities for Poisson-Laguerre semigroups

2015/11/12 by Garrigos, Gustavo, Hartzstein, Silvia, Signes, Teresa +1 · 1 citation
#33C45 #35C15 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1511.03966

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^-t√(L). First, we find the largest space of initial data f so that e^-t√(L)f(x)→ f(x) at a.e. x. Secondly, we characterize the largest class of weights w which admit 2-weight inequalities of the form ‖sup_0

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• Pointwise convergence to initial data of heat and Hermite-heat equations in Modulation Spaces

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