Vol. 65, No. 1, 1976

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Sobolev approximation by a sum of subalgebras on the circle

John Brady Garnett and Anthony G. O’Farrell

Vol. 65 (1976), No. 1, 55–63

Let ψ be an orientation-reversing homeomorphism of the unit circle onto itself. We consider approximation in certain Sobolev norms by functions of the form f(z) + g(ψ), where f and g are polynomials. The methods involve conformal welding and Hardy space theory. We construct a Jordan arc of positive continuous analytic capacity such that the harmonic measures for the two complementary domains are mutually absolutely continuous.

Mathematical Subject Classification
Primary: 30A82, 30A82
Received: 14 April 1975
Revised: 18 February 1976
Published: 1 July 1976
John Brady Garnett
Department of Mathematics
University of California
Los Angeles CA 90024
United States
Anthony G. O’Farrell