Zero sets and extensions of bounded holomorphic functions in polydiscs

Chee, P. S.

doi:10.1090/S0002-9939-1976-0422678-5

Zero sets and extensions of bounded holomorphic functions in polydiscs
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by P. S. Chee PDF

Proc. Amer. Math. Soc. 60 (1976), 109-115 Request permission

Abstract:

A sufficient condition for a hypersurface in a polydisc ${U^n}$ to be the zero set of an ${H^\infty }({U^n})$ function is proved. This strengthens a result of Zarantonello and generalizes a result of Rudin. Using this result and a result of Andreotti and Stoll, a partial extension of Alexander’s theorem on extension of bounded holomorphic functions from a hypersurface of ${U^n}$ to ${U^n}$ is obtained. Finally, a generalization of Cima’s extension theorem for ${H^p}$ functions is given.

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