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Correction to "Removable singularities for analytic or subharmonic functions"

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Correction to "Removable singularities for analytic or subharmonic functions"

18:1 (1980) l l l , by

Robert Kaufman and Jang-Mei W u

The

construction

of the partition of unity (q~) cannot be used as the assertion

ri/16<=rj/4

on page 111, line 5 is invalid. Instead we can cover each ball

B(zi, ri)

with 16 dyadic squares with sides between

ri/2

and

ri,

and apply the construction by R. Harvey and J. Polking (Acta Mathematica 125 (1970), p. 43). This succeeds for operators of degree 1 or 2, because there is a bound on the number of functions q~k arising from each ball, and because the first and second order partial derivatives are bounded by

O(r? 1)

and

O(r?~),

respectively.

Received April 2, 1982

University of Illinois

Department of Mathematics Urbana, Ill. 61 801

USA

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