Representation via ∂-equation
The Fefferman-Stein decomposition theorem for BMOA is to say that every BMOA-function f can be written as the sum f 1∔f 2 where f 1, f 2 ∈ H and Ref j ∈ L∞(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 p ∩ H ∞ and Q p, and then show the interpolation theorem for Q p ∩ H ∞.
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