A factorization theorem in 𝐻¹(𝑈³)

Miles, Joseph

doi:10.1090/S0002-9939-1975-0374459-8

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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A factorization theorem in $H^{1}(U^{3})$
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by Joseph Miles

Proc. Amer. Math. Soc. 52 (1975), 319-322

DOI: https://doi.org/10.1090/S0002-9939-1975-0374459-8

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Abstract:

It is shown that there exists $f\epsilon {H^1}({U^3})$ which is not the product of two functions in ${H^2}({U^3})$. This partially answers a question posed by W. Rudin.

References

Walter Rudin, Zeros and factorizations of holomorphic functions, Bull. Amer. Math. Soc. 72 (1966), 1064–1067. MR 197771, DOI 10.1090/S0002-9904-1966-11647-6
Walter Rudin, Function theory in polydiscs, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0255841