科研之友
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摘要
Consider the direct product manifold M-1 x . . . x M-n, where M-i (1 <= i <= n) are connected complete non-compact Riemannian manifolds satisfying the volume doubling property and Gaussian or sub-Gaussian estimates for the heat kernel. We obtain weak type (1, 1) (so L-p-boundedness with 1 < p < 2) for the Riesz transform. As a consequence, we find that neither heat kernel Gaussian estimates nor sub-Gaussian estimates are necessary for weak (1, 1) property of Riesz transform.
- 出版日期2018-4
- 单位复旦大学
