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Coupling and Harnack inequalities for Sierpinski carpets
Author(s):
Martin
T.
Barlow;
Richard
F.
Bass
Journal:
Bull. Amer. Math. Soc.
29
(1993),
208-212.
MSC (1991):
Primary 60B99;
Secondary 60J35
MathSciNet review:
1215306
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References |
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Additional information
References:
- [1]
- M. T. Barlow and R. F. Bass, The construction of Brownian motion on the Sierpinski carpet, Ann. Inst. H. Poincar\'e Probab. Statist. \textbf{25} (1989), 225--257. MR 1023950
- [2]
- M. T. Barlow and R. F. Bass, Local times for Brownian motion on the Sierpinski carpet, Probab. Theory Related Fields \textbf{85} (1990), 91--104. MR 1044302
- [3]
- M. T. Barlow and R. F. Bass, On the resistance of the Sierpinski carpet, Proc. Roy. Soc. London Ser. A \textbf{431} (1990), 345--360. MR 1080496
- [4]
- M. T. Barlow and R. F. Bass, Transition densities for Brownian motion on the Sierpinski carpet, Probab. Theory Related Fields \textbf{91} (1992), 307--330. MR 1151799
- [5]
- R. F. Bass and P. Hsu, Some potential theory for reflecting Brownian motion in H\"older and Lipschitz domains, Ann. Probab. \textbf{19} (1991), 486--508. MR 1106272
- [6]
- D. Ben-Avraham and S. Havlin, Diffusion in disordered media, Adv. Phys. \textbf{36} (1987), 695--798. MR
- [7]
- E. B. Davies, Heat kernels and spectral theory, Cambridge Univ. Press, Cambridge, 1989. MR 990239
- [8]
- S. Kusuoka and X. Y. Zhou, Dirichlet form on fractals\,\RM : Poincar\'e constant and resistance, Probab. Theory Related Fields \textbf{93} (1992), 169--196. MR 1176724
- [9]
- I. McGillivray, Some applications of Dirichlet forms in probability theory, Ph.D.~ dissertation, Cambridge Univ., 1992. MR
- [10]
- H. Osada, Isoperimetric dimension and estimates of heat kernels of pre-Sierpinski carpets., Probab. Theory Related Fields \textbf{86} (1990), 469--490. MR 1074740
- [11]
- V. G. Maz'ja, Sobolev spaces, Springer-Verlag, New York, 1985. MR 817985
- [12]
- N. Th. Varopoulos, Hardy-Littlewood theory for semigroups, J. Funct. Anal. \textbf{63} (1985), 240--260. MR 803094
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Additional Information:
DOI:
10.1090/S0273-0979-1993-00424-5
PII:
S 0273-0979(1993)00424-5
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