Factorization of some Hardy type spaces of holomorphic functions

2014/06/20 by Aline Bonami, Bonami, Aline, Luong Dang Ky +1
Mathematics · #32A35 #42B35 #47B35 #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #math.CA #math.CV #msc:32A35 #msc:42B35 #msc:47B35

paper · pdf · doi:10.48550/arxiv.1406.5438

C. R. Math. Acad. Sci. Paris (to appear)

arxiv created 2015/04/09 · arxiv updated 2015/04/10

Abstract

We prove that the pointwise product of two holomorphic functions of the upper half-plane, one in the Hardy space \mathcal H¹, the other one in its dual, belongs to a Hardy type space. Conversely, every holomorphic function in this space can be written as such a product. This generalizes previous characterization in the context of the unit disc.

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