Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-12T21:46:33.798Z Has data issue: false hasContentIssue false
  • English
  • Français

Minimal fine derivatives and Brownian excursions

Published online by Cambridge University Press:  22 January 2016

Krzysztof Burdzy
Krzysztof Burdzy*
Affiliation:
Department of Mathematics University of Washington, Seattle, WA 98195, U.S.A.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The paper will present some basic properties of minimal fine derivatives which seems to be a new concept (or at least a new combination of well-known ones). Why is it worthwhile to study this new concept? Why hasn’t it been done earlier?

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 119 , September 1990 , pp. 115 - 132
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1990

References

[1] Burdzy, K., Brownian excursions and minimal thinness, Part III, Applications to the angular derivative problem, Math. Z., 192 (1986), 89–107.Google Scholar
[2] Burdzy, K., “Multidimensional Brownian Excursions and Potential Theory,” Longman London (1987).Google Scholar
[3] Burdzy, K. and Williams, R. J., On Brownian escursions in Lipschitz domains, Part I, Local path properties, Trans. Amer. Math. Soc., 298 (1986), 289–306.Google Scholar
[4] Davis, B., Brownian motion and analytic functions, Ann. Probab., 7 (1979), 913–932.CrossRefGoogle Scholar
[5] Doob, J. L., “Classical Potential Theory and Its Probabilistic Counterpart,” Springer, New York (1984).Google Scholar
[6] Durrett, R., “Brownian Motion and Martingales in Analysis,” Wadsworth, Belmont (1984).Google Scholar
[7] Essén, M. and Jackson, H. L., On the covering properties of certain exceptional sets in a halfspace, Hiroshima Math. J., 10 (1980), 233–262.CrossRefGoogle Scholar
[8] Jackson, H. L., Some remarks on angular derivatives and Julia’s Lemma, Can. Math. Bull., 9 (1965), 233–241.CrossRefGoogle Scholar
[9] Jackson, H. L., On the boundary behaviour of BLD functions and some applications, Bull. Cl. Sc. Acad. R. Belgique, 66 (1980), 223–239.Google Scholar
[10] Maisonneuve, B., Exit systems, Ann. Probab., 3 (1975), 399–411.CrossRefGoogle Scholar
[11] Nairn, L., Sur le rôle de la frontière de R. S. Martin dans la théorie du potential, Ann. Inst. Fouriere, Grenoble, 7 (1957), 183–281.Google Scholar
[12] Pommerenke, C., “Univalent Functions,” Vandenhoeck and Ruprecht, Göttingen, (1975).Google Scholar
[13] Rodin, B. and Warschawski, S. E., Extremal length and univalent functions. I. The angular derivative, Math. Z., 153 (1977), 1–17.Google Scholar