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Potential theory of Schrödinger operator based on fractional Laplacian. (English) Zbl 0996.31003

The authors study the potential theory of Schrödinger operators based on fractional Laplacians in Euclidean spaces of arbitrary dimension. The starting point of this paper is a conditional gauge theorem for small balls, which is an easy consequence of the 3G inequality.

MSC:

31B05 Harmonic, subharmonic, superharmonic functions in higher dimensions
31B15 Potentials and capacities, extremal length and related notions in higher dimensions
60J45 Probabilistic potential theory
35J10 Schrödinger operator, Schrödinger equation
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