Given a formally integrable almost complex structure $X$ defined on the closure of a bounded domain $D \subset \mathbb C^n$, and provided that $X$ is sufficiently close to the standard complex structure, the global Newlander-Nirenberg problem asks whether there exists a global diffeomorphism defined on $\overline D$ that transforms $X$ into the standard complex structure, under certain geometric and regularity assumptions on $D$. In this talk I will present my recent result on the ½ estimate for global Newlander-Nirenberg problem on strongly pseudoconvex domains. The main ingredients in our proof are the construction of Moser-type smoothing operators on bounded Lipschitz domains using Littlewood-Paley theory and a convergence scheme of KAM type.