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Lebesgue points via the Poincare inequality Karak Nijjwal博士, 芬兰于韦斯屈莱大学

报告时间:2014年9月17日(周三)下午16:00 -17:00报告地点:北航数学与系统科学ag平台app下载主 213学术交流厅报告摘要: By the classical Lebesgue differentiation theorem almost every point is a Lebesgue point for a locally integrable function. It is natural to expect that if the function in question is more regular, then the exceptional set is smaller. In this talk, I will first explain how one gets the existence of Lebesgue points of a Sobolev function $W^{1,p}$ in $R^n$ almost everywhere using a chaining argument and Poincare inequality. Then I will explain the results in the literature for Lebesgue points of a Sobolev function in $R^n$ and in metric spaces. Then I will discuss about Lebesgue points of a locally integrable function $u$ which together with $g/in L^Q$ satisfies a $Q$-Poincare inequality in a $Q$-doubling metric space, $Q>1.$ This is a joint work with Prof. Pekka Koskela.

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