Minimum Solution of ∂k + 1 and Middle Hankel Operators

We formulate the solution of the equation ∂k + 1F = f with minimum L2 norm and characterize the symbol functions so that the corresponding middle Hankel operators are bounded, compact, and belong to the Schatten p-class (p ≥ 1). This generalizes the earlier results by Peng-Rochberg-Wu. The approach is inspired by a recent work of Luecking.