In this paper, for the 1-D semilinear wave equation \(\partial _t^2u - \partial _x^2u + {\mu \over t}{\partial _t}u = |u{|^p}\) with scaling invariant damping, where t ≥ 1, p > 1 and \(\mu \in (0,1) \cup \left(1,{4 \over 3}\right)\) , we establish the global weighted space-time estimates as well as the global existence of small data weak solution u when the nonlinearity power p is larger than some critical power pcrit(μ) Our proof is based on a class of new weighted Strichartz estimates with the weight \({t^\theta}|{(1 - \mu)^2}{t^{{2 \over {|1 - \mu |}}}} - {x^2}{|^\gamma}\) (θ > 0 and γ > 0 are appropriate constants) for the solution of linear generalized Tricomi equation \(\partial _t^2\phi - {t^m}\partial _x^2\phi = 0\) with m being any fixed positive number.
