Estimates and structure of α-harmonic functions

  title={Estimates and structure of α-harmonic functions},
  author={Krzysztof Bogdan and Tadeusz Kulczycki and Mateusz Kwasnicki},
We prove a uniform boundary Harnack inequality for nonnegative harmonic functions of the fractional Laplacian on arbitrary open sets D. This yields a unique representation of such functions as integrals against measures on Dc∪{∞} satisfying an integrability condition. The corresponding Martin boundary of D is a subset of the Euclidean boundary determined by an integral test. 1 Main results and introduction Let d = 1, 2, . . ., and 0 < α < 2. The boundary Harnack principle (BHP) for nonnegative… CONTINUE READING
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