## 摘要

Consider an (L, α)-superdiffusion X on ℝ^{d}, where L is an uniformly elliptic differential operator in ℝ^{d}, and 1 < α < 2. The G-polar sets for X are subsets of ℝ × ℝ^{d} which have no intersection with the graph G of X, and they are related to the removable singularities for a corresponding nonlinear parabolic partial differential equation. Dynkin characterized the G-polarity of a general analytic set A ⊂ ℝ × ℝ^{d} in term of the Bessel capacity of A, and Sheu in term of the restricted Hausdorff dimension. In this paper we study in particular the G-polarity of sets of the form E × F, where E and F are two Borel subsets of ℝ and ℝ^{d} respectively. We establish a relationship between the restricted Hausdorff dimension of E × F and the usual Hausdorff dimensions of E and F. As an application, we obtain a criterion for G-polarity of E × F in terms of the Hausdorff dimensions of E and F, which also gives an answer to a problem proposed by Dynkin in the 1991 Wald Memorial Lectures.

原文 | English |
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頁（從 - 到） | 3721-3728 |

頁數 | 8 |

期刊 | Proceedings of the American Mathematical Society |

卷 | 127 |

發行號 | 12 |

出版狀態 | Published - 1 十二月 1999 |