报告题目： Restrictions for solutions of　the heat equations with Newton-Sobolev data on metric measure spaces 报 告 人： 袁文 教授 报告人所在单位： 北京师范大学 报告日期： 2017-04-27 星期四 报告时间： 10:00-11:00 报告地点： 光华东主楼1501 报告摘要： On a complete doubling metric measure space $(X,d,\mu)$ supporting the weak Poincaré inequality, by  establishing some capacitary strong-type inequalities for the Hardy-Littlewood maximal operator, we characterize the measure $\nu$ on the space $X\times(0,\infty)$ so that the mapping $f\mapsto \int_{X} p_{t}(\cdot,y)f(y) d\mu(y)$, is bounded from the Newton-Sobolev space $N^{1,p}(X)$ with $p\in [1,\infty)$ into the Lebesgue space $L^q(X\times(0,\infty),\nu)$ with $q\in(0,\infty)$, where the kernels $p_t$  are some generalized heat kernels. This result generalizes the Carleson embeddings obtained in [J. Differential Equations 224 (2006), 277-295], and also provides a priori estimate of the solution of heat equations with Newton-Sobolev data on many metric measure spaces $X$ such as complete Riemannian manifolds and fractals. 本年度学院报告总序号： 59