| Towards an L^p Potential Theory for Sub-Markovian Semigroups： Kernels and Capacities |
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| 作者姓名： | Niels JACOB Rene L. SCHILLING |
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| 作者单位： | [1]Department of Mathematics, University of Wales Swansea, Singleton Park, Swansea SA 2 8 PP, United Kingdom [2]FB 12 - Mathematik, Philipps-Universitat Marburg, D-35032 Marburg, Germany |
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| 摘 要： | We study in fairly general measure spaces （X,μ） the （non-linear） potential theory of L^p sub-Markovian semigroups which are given by kernels having a density with respect to the underlying measure. In terms of mapping properties of the operators we provide sufficient conditions for the existence （and regularity） of such densities. We give various （dual） representations for several associated capacities and, in the corresponding abstract Bessel potential spaces, we study the role of the truncation property. Examples are discussed in the case of R^n where abstract Bessel potential spaces can be identified with concrete function spaces.
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| 关 键 词： | 非线性位势理论 （r p）容量 Bessel位势空间 γ转化 次Markovian半群 |
| 收稿时间： | 2004-05-20 |
| 修稿时间： | 2004-05-202004-09-02 |
Towards an L
p
Potential Theory for Sub–Markovian Semigroups: Kernels and Capacities |
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| Niels JACOB Rene L. SCHILLING.Towards an L
p
Potential Theory for Sub–Markovian Semigroups: Kernels and Capacities[J].Acta Mathematica Sinica,2006,22(4):1227-1250. |
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| Authors: | Niels Jacob René L Schilling |
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| Institution: | 1. Department of Mathematics, University of Wales Swansea, Singleton Park, Swansea SA2 8PP, United Kingdom
2. FB 12—Mathematik, Philipps-Universit?t Marburg, D-35032, Marburg, Germany
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| Abstract: | We study in fairly general measure spaces (X, μ) the (non–linear) potential theory of L
p
sub–Markovian semigroups which are given by kernels having a density with respect to the underlying measure. In terms of
mapping properties of the operators we provide sufficient conditions for the existence (and regularity) of such densities.
We give various (dual) representations for several associated capacities and, in the corresponding abstract Bessel potential
spaces, we study the role of the truncation property. Examples are discussed in the case of ℝ
n
, where abstract Bessel potential spaces can be identified with concrete function spaces. |
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| Keywords: | nonlinear potential theory (r p)– capacity Bessel potential space gamma– transform sub– Markovian semigroup |
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