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on Rx,y×Rt, with initial data φ in the space E∩P , where E = {f : f ∈ L2, ∂xf ∈ L2, ∂y∂−1 x f ∈ L2} and P = {f : yf ∈ L2}. The main result in [CKS], ([CKS, Th. 1]) is a weak form of local in time well-posedness for data which is small in E ∩ P . Unfortunately, A. Ionescu discovered a counterexample to the main estimate used in [CKS] to establish Theorem 1. The example exhibits a logarithmic divergence in the estimate, which shows that the proof of Theorem 1 in [CKS] is incorrect. The same applies to Theorem 2 in [CKS], which claims the corresponding result at an smaller regularity level. The authors are very grateful to A. Ionescu for pointing out this mistake. In the paper [CIKS], joint with A. Ionescu, we describe the counterexample in detail ([CIKS, §1.1]) and succeed in obtaining a strengthening of Theorem 1 in [CKS], namely the strong form of local in time well-posedness for small data in E ∩ P ([CIKS, Th. 1.1]). The logarithmic divergence is avoided in [CIKS] by introducing new resolution spaces, inspired by those used by Ionescu–Kenig ([IK1,2,3]) in works on the Benjamin–Ono and the Schrödinger map problems. It seems likely (but not particularly interesting at this point in time) that the methods developed in [CIKS] would also provide a correct (and similarly strengthened) version of Theorem 2 in [CKS].

Errata to “Low Regularity Solutions for the Kadomtsev–Petviashvili I Equation”, GAFA, Geom. Funct. Anal. 13 (2003), 737-794