Abstract:

Riesz transform measures the behavior of gradient operator and the square roof of the Laplacian operator, is deeply related to the quasi-isometries of manifolds. In this talk, we shall review recent developments on the Riesz transform, and its relation to harmonic functions and heat kernels. Generally speaking, the behavior of heat kernel and harmonic functions, e.g. L^p-regularity, whether there are sublinear growth harmonic functions, etc., are closely related to the behavior of Riesz transforms. 

Zoom Meeting ID: 181 155 584