A factorization theorem in 𝐻¹(𝑈³)

Miles, Joseph

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

A factorization theorem in $H\sp{1}(U\sp{3})$

Author: Joseph Miles
Journal: Proc. Amer. Math. Soc. 52 (1975), 319-322
MSC: Primary 32A10; Secondary 30A78, 46J15
DOI: https://doi.org/10.1090/S0002-9939-1975-0374459-8
MathSciNet review: 0374459
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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.

[1] Walter Rudin, Zeros and factorizations of holomorphic functions, Bull. Amer. Math. Soc. 72 (1966), 1064–1067. MR 0197771, https://doi.org/10.1090/S0002-9904-1966-11647-6
[2] Walter Rudin, Function theory in polydiscs, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0255841