Estimates and structure of α-harmonic functions

@inproceedings{Bogdan2006EstimatesAS,
  title={Estimates and structure of α-harmonic functions},
  author={Krzysztof Bogdan and Tadeusz Kulczycki and Mateusz Kwasnicki},
  year={2006}
}
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
Highly Cited
This paper has 27 citations. REVIEW CITATIONS

From This Paper

Topics from this paper.
19 Citations
36 References
Similar Papers

References

Publications referenced by this paper.
Showing 1-10 of 36 references

The boundary Harnack principle for the fractional Laplacian

  • K. Bogdan
  • Studia Math. 123
  • 1997
Highly Influential
7 Excerpts

Hitting times and potentials for recurrent stable processes

  • S. Port
  • J. Analyse Math. 20
  • 1967
Highly Influential
6 Excerpts

Representation of α-harmonic functions in Lipschitz domains

  • K. Bogdan
  • Hiroshima Math. J. 29
  • 1999
Highly Influential
4 Excerpts

W

  • J. Bliedtner
  • Hansen, Potential Theory Springer-Verlag Berlin…
  • 1986
Highly Influential
4 Excerpts

Landkof, Foundations of modern potential theory Springer-Verlag, New York

  • N S.
  • 1972
Highly Influential
5 Excerpts

Uniform boundary Harnack principle and generalized triangle property

  • W. Hansen
  • J. Funct. Anal. 226
  • 2005

Similar Papers

Loading similar papers…