## 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
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 $H_Ï$-norm estimates of the corona solutions for $Ï\inÎ_2\cap\nabla_2$. Moreover we also show that the $Î_2$-condition is necessary in some interesting cases.