Correction to "Primary solutions of general Beltrami equations"

Abstract

As was noticed by several readers, I was not sufficiently careful in the formulation and the proof of Proposition 2 in [6]. The correct Beltrami equation for the function G(ζ)—in the notation of [6], used throughout in this correction—is more complicated than stated in [6] and the use of its correct, in particular, quasilinear, form in a proof of the Theorem in [6] should be reconsidered. However the main Theorem as stated and the factorisation strategy for the proof proposed is valid. Since the problem of “primary” solutions for Beltrami equations, started in the present form by Iwaniec et al. [7], aroused a rather long list of publications, extensively referred to, in particular, in the recent monograph [1], it seems proper to reconsider the topic from another perspective. The corresponding paper is in preparation. Below we sketch another approach to the main theorem in [6]. The theorem reads as follows.