Binder, Ilia Phase transition for the universal bounds on the integral means spectrum. (English) Zbl 1171.30305 Nonlinearity 22, No. 8, 1857-1867 (2009). Summary: We generalize Beurling’s estimate on the rate of decay of harmonic measure near a boundary point with given rotation. The generalization allows us to establish the existence of phase transition for the universal bounds on the integral means mixed spectrum of bounded simply connected domains. Cited in 1 Document MSC: 30C75 Extremal problems for conformal and quasiconformal mappings, other methods 30C35 General theory of conformal mappings 31A15 Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions Keywords:rate of decay of harmonic measure near a boundary point; Beurling’s estimate PDFBibTeX XMLCite \textit{I. Binder}, Nonlinearity 22, No. 8, 1857--1867 (2009; Zbl 1171.30305) Full Text: DOI Link