Martin boundary points of a John domain and unions of convex sets

Journal of the Mathematical Society of Japan

Volumn 58, Issue 1, 2006, Pages 247-274

  Aikawa, Hiroaki ^a   Hirata, Kentaro ^a   Lundh, Torbjörn ^b  

^a HOKKAIDO UNIVERSITY   (Japan)

^b CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

Carleson estimate; Convex set; Domar's theorem; John domain; Martin boundary; Quasihyperbolic metric; Tract; Weak boundary Harnack principle

Indexed keywords

EID: 33645148792     PISSN: 00255645     EISSN: None     Source Type: Journal    
DOI: 10.2969/jmsj/1145287101     Document Type: Article

References (21)

1. H. Aikawa, Integrability of superharmonic functions in a John domain, Proc. Amer. Math. Soc., 128 (2000), no. 1, 195-201.
2. H. Aikawa, Boundary Harnack principle and Martin boundary for a uniform domain, J. Math. Soc. Japan, 53 (2001), no. 1, 119-145.
3. H. Aikawa, T. Lundh and T. Mizutani, Martin boundary of a fractal domain, Potential Anal., 18 (2003), 311-357.
4. H. Aikawa and N. Shanmugalingam, Carleson type estimates for p-harmonic functions and the conformal Martin boundary of John domains in metric measure spaces, Michigan Math. J., 53 (2005), no. 1, 165-188.
5. A. Ancona, Une propriété de la compactification de Martin d'un domaine euclidien, Ann. Inst. Fourier (Grenoble), 29 (1979), no. 4, 71-90.
6. A. Ancona, Régularité d'accès des bouts et frontière de Martin d'un domaine euclidien, J. Math. Pures Appl., 63 (1984), no. 2, 215-260.
7. A. Ancona, Sur la frontière de Martin des domaines de Denjoy, Ann. Acad. Sci. Fenn. Ser. A I Math., 15 (1990), no. 2, 259-271.
8. D. H. Armitage and S. J. Gardiner, Classical potential theory, Springer, London, 2001.
9. R. F. Bass and K. Burdzy, A boundary Harnack principle in twisted Holder domains, Ann. of Math. (2), 134 (1991), no. 2, 253-276.
10. n, Ark. Mat., 18 (1980), no. 1, 53-72.
11. n dont le bord est inclus dans une hyper-surface lipschitzienne, Ark. Mat., 27 (1989), no. 1, 29-48.
12. M. C. Cranston and T. S. Salisbury, Martin boundaries of sectorial domains, Ark. Mat., 31 (1993), no. 1, 27-49.
13. Y. Domar, On the existence of a largest subharmonic minorant of a given function, Ark. Mat., 3 (1957), 429-440.
14. L. Fejes, Über eine Abschätzung des kürzesten Abstandes zweier Punkte eines auf einer Kugelfläche liegenden Punktsystems, Jber. Deutsch. Math. Verein., 53 (1943), 66-68.
15. S. Friedland and W. K. Hayman, Eigenvalue inequalities for the Dirichlet problem on spheres and the growth of subharmonic functions, Comment. Math. Helv., 51 (1976), no. 2, 133-161.
16. F. W. Gehring and O. Martio, Lipschitz classes and quasiconformal mappings, Ann. Acad. Sci. Fenn. Ser. A I Math., 10 (1985), 203-219.
17. W. K. Hayman and P. B. Kennedy, Subharmonic functions. Vol. I, Academic Press, London, 1976.
18. A. Lömker, Martin boundaries of quasi-sectorial domains, Potential Anal., 13 (2000), no. 1, 11-67.
19. R. S. Martin, Minimal positive harmonic functions, Trans. Amer. Math. Soc., 49 (1941), 137-172.
20. W. Smith and D. A. Stegenga, Hölder domains and Poincaré domains, Trans. Amer. Math. Soc., 319 (1990), no. 1, 67-100.
21. W. Smith and D. A. Stegenga, Exponential integrability of the quasi-hyperbolic metric on Holder domains, Ann. Acad. Sci. Fenn. Ser. A I Math., 16 (1991), no. 2, 345-360.