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The modulus of Rudin-Carleson extensions

Authors:	Josip Globevnik

Institution:	(1) Institute of Mathematics, Physics and Mechanics, E. K. University of Ljubljana, Ljubljana, Yugoslavia

Abstract:	We prove the followingTheorem. LetF be a closed subset of the unit circleT which has Lebesgue measure zero. Suppose thatp is a smooth positive function onT. GivenfC(F) which satisfies\|f(s)\|p(s) (sF) and a neighbourhoodU ofF there is an extension $\tilde f$ off in the disc algebra such that $\|\tilde f(z)\| \leqslant p(z) (z \in U)$ and $\|\tilde f(z)\| = p(z) (z \in T\backslash U)$ .

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