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Phase transition for the universal bounds on the integral means spectrum. (English) Zbl 1171.30305

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.

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
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