摘要:  It is well known that, due to the lackness of some classical tools (derivatives, Fourier analytic tools et al.) on metric measure spaces, to develop function spaces with (higher order) smoothness (like Sobolev spaces, Besov spaces and Triebel-Lizorkin spaces) on such underlying spaces, one main difficulty is to find a suitable way to characterize their smoothness. In this talk, we present a series of new characterizations of Sobolev, Besov and Triebel-Lizorkin spaces via differences of ball averages.  Since these characterizations do not rely on the differential structure of Euclidean spaces, they provide some new ways to introduce these spaces on metric measure spaces.

报告人：袁文教授，北京师范大学