The Corona Type Decomposition of Hardy-Orlicz Spaces

J. Math. Sci. Univ. Tokyo
Vol. 10 (2003), No. 1, Page 171--185.

Imai, Ryuta
The Corona Type Decomposition of Hardy-Orlicz Spaces
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Abstract:
The \hpp -corona type problem in several complex variables has been solved affirmatively by Amar \cite{amar}, Andersson \cite{ander}, Andersson-Carlesson [3, 4], Krantz-Li \cite{krali} and others. In particular, Andersson-Carlsson \cite{andercarl2} proved the \hpp -norm estimates of the corona solutions which are constructed by a concrete integral representation formula. In this paper, we give some Orlicz space versions for interpolation theorems of Marcinkiewicz type and prove the $H_φ$-norm estimates of the corona solutions for $φ\inΔ_2\cap\nabla_2$. Moreover we also show that the $Δ_2$-condition is necessary in some interesting cases.

Mathematics Subject Classification (1991): 42B25, 32A35, 32A40
Mathematical Reviews Number: MR1963802

Received: 2002-01-07