Beurling--Carleson Endpoint Counterexamples: Singular Inner Functions and a Semilinear Equation

Pengcheng Fang, Yixin He

We settle two endpoint problems for Beurling--Carleson support conditions. For $0<s<\frac{1}{2}$ and $\theta =\frac{1-2s}{1-s}$, we construct a nonatomic singular probability measure $\mu$, su…