Semi-linear wave models with power non-linearity and scale-invariant time-dependent mass and dissipation, II

This paper is a continuation of our recent paper. We will consider the semi-linear Cauchy problem for wave models with scale-invariant time-dependent mass and dissipation and power non-linearity. The goal is to study the interplay between the coefficients of the mass and the dissipation term to prove global existence (in time) of small data energy solutions assuming suitable regularity on the L2 scale with additional L1 regularity for the data. In order to deal with this L2 regularity in the non-linear part, we will develop and employ some tools from Harmonic Analysis.