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Abstract: 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.