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The current version of the introduction "Grunsky matrices, or "Grunsky operatosr" gives the impression that these are the same things under different names. That is not correct.
It seems natural, having named the operators, to say something about the spaces on which those operators are defined.
The introduction mentions the matrices, then the operators, introduces the inequalities, then goes back to the operators in the last couple of sentences. Why not group the concepts together?
The section Grunsky inequalities states the inequality without explicitly saying that it may or may not hold for the Grunsky matrix of f. This would be a point at which to repeat as a formal statement that the inequality is equivalent to univalence of f.
The section Milin's proof of Grunsky inequalities again needs to explicitly state what is being proved: here that univalence implies the inequality
Under Pairs of univalent functions it might help to make clear that in this case the matrix is now doubly infinite.
In Unitarity the first sentence reads as if it were a definition of unitarity. It needs to be stated explicitly as a theorem. Is it supposed to be obvious, or is the proof to be supplied, or in a reference? Similarly, the second sentence, beginning "So" needs a proof or a reference. "Quasicircle" is not defined in the article, nor is there any article to link it to. The logical status of the rest of the section is not clear: is it intended to prove unitarity, and if so, how exactly does it link to univalence?
Under Beurling transform T sub Omega appears to change to T sub f without warning. This is especially confusing since f is noit uniquely determined by Omega. Is it the case that T sub f actually depends only on f, or simply that the statements are independent of the choice of f?
Similar remarks apply to "the" Grunsky operator defined as such in the next section. If independent of f, say so explicitly.
The final section Singular integral operators on a closed curve is clearly incomplete.