Weak-Type estimates for the metaplectic representation restricted to the shearing and Dilation subgroup of SL(2, ℝ)

Abstract

We consider the subgroup G of SL(2, ℝ) consisting of shearing and dilations, and we study the decay at infinity of the matrix coefficients of the metaplectic representation restricted to G. We prove weak-type estimates for such coefficients, which are uniform for functions in the modulation space M1. This work represents a continuation of a project aiming at studying weak-type and Strichartz estimates for unitary representations of non-compact Lie groups.