期刊文献+
任意字段
题名或关键词
题名
关键词
文摘
作者
第一作者
机构
刊名
分类号
参考文献
作者简介
基金资助
栏目信息

Towards an L^p Potential Theory for Sub-Markovian Semigroups:Kernels and Capacities

Towards an L^p Potential Theory for Sub-Markovian Semigroups:Kernels and Capacities
原文传递
导出
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. 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.
作者 Niels JACOB RenéL.SCHILLING
机构地区 Department of Mathematics FB
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2006年第4期1227-1250,共24页 数学学报（英文版）
关键词 nonlinear potential theory （r p）-capacity Bessel potential space gamma.transform sub-Markovian semigroup nonlinear potential theory, （r,p）-capacity, Bessel potential space, gamma.transform, sub-Markovian semigroup
分类号 O152.7 [理学—基础数学]
  • 相关文献

参考文献47

  • 1Hoh, W., Jacob, N.: Towards an L^p potential theory for sub-Markovian semigroups: variational inequalities and balayage theory. J. Evol. Equ., 4, 297-312 (2004)
  • 2Malliavin, P.: Implicit functions in finite corank on the Wiener space, Ito, K. (ed.): Proceedings Taniguchi Syrup. Stoch. Anal. Katata and Kyoto 1982, Math. Libr. 32, North-Holland, Amsterdam, 369-386, 1984
  • 3Fukushima, M.: Two topics related to Dirichlet forms: quasi-everywhere convergence and additive functionals, Dell'Antonio, G., Mosco, U. (eds.): Dirichlet Forms, Lect. Notes Math. 1563, Springer, Berlin, 21-53,1993
  • 4Fukushima, M., Kaneko, H.: On (r,p)-capacities for general Markovian semigroups, Albeverio, S. (ed.):Infinite dimensional analysis and stochastic processes, Res. Notes Math. 124, Pitman, Boston (MA), 41-47,1985
  • 5Fukushima, M., Oshima, Y., Takeda, M.: Dirichlet Forms and Symmetric Markov Processes, Stud. Math.19, de Gruyter, Berlin, 1994
  • 6Kazumi, T., Shigekawa, I.: Measures of finite (r,p)-energy and potentials on a separable metric space,Azema, J., Meyer, P. A., Yor, M. (eds.): Seminaire de Probabilites XXVI, Lect. Notes Math. 1526, Springer,Berlin, 415-444, 1992
  • 7Maz'ya, V. G., Havin, V. P.: Nonlinear potential theory. Russ. Math. Surv., 27, 71-148 (1972)
  • 8Maz'ja (Maz'ya), V.G., Sobolev Spaces, Series in Soviet Math., Springer, Berlin, 1985
  • 9Mizuta, Y.: Potential theory in Euclidean spaces, GAKUTO Int. Ser., Math. Sci. Appl. 6, Gakkotosho,Tokyo, 1996
  • 10Adams, D. R., Hedberg, L. I.: Function Spaces and Potential Theory, Grundlehren Math. Wiss. 314,Springer, Berlin 1999 (corr. 2nd printing)
Acta Mathematica Sinica,English Series
2006年 第4期

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部