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] W. Rudin, Zeros and factorizations of holomorphic functions, Bull Amer. Math. Soc. 72 (1966), 1064-1067. MR 33 #5934. MR 0197771 (33:5934)
[2] -, Function theory in polydiscs, Benjamin, New York, 1969. MR 41 #501. MR 0255841 (41:501)