A pure smoothness condition for Radó’s theorem for α-analytic functions
Let (Formula presented.) be a bounded, simply connected ℂ-convex domain. Let α ∈ ℤ+ n and let f be a function on Ω which is separately (Formula presented.) -smooth with respect to zj (by which we mean jointly (Formula presented.) -smooth with respect to Rezj, Imzj). If f is α-analytic on Ω\f−1(0), then f is α-analytic on Ω. The result is well-known for the case αi = 1, 1 ⩽ i ⩽ n, even when f a pri