Representation via ∂-equation

Part of the Lecture Notes in Mathematics book series (LNM, volume 1767)


The Fefferman-Stein decomposition theorem for BMOA is to say that every BMOA-function f can be written as the sum f 1f 2 where f 1, f 2H and Ref jL∞(T). The main aim of this chapter is to extend this result to Q p, p ∈ (0,1). This aim will be realized via: introducing Q p(T), the non-holomorphic version of Q p; finding the Q p(T) ∩ L (T)-solutions to the ∂-equation; and presenting the Fefferman-Stein type decomposition for Q p. As certain applications of the ∂-equation, we give the corona theorems for both Q pH and Q p, and then show the interpolation theorem for Q pH .


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© Springer-Verlag Berlin Heidelberg 2001

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