期刊
COLLOQUIUM MATHEMATICUM
卷 118, 期 2, 页码 685-704出版社
ARS POLONA-RUCH
DOI: 10.4064/cm118-2-20
关键词
heat kernels; Riesz transform; Sobolev type inequalities
类别
We show that the L(p) boundedness, p > 2, of the Riesz transform on a complete non-compact Riemannian manifold with upper and lower Gaussian heat kernel estimates is equivalent to a certain form of Sobolev inequality. We also characterize in such terms the heat kernel gradient upper estimate on manifolds with polynomial growth.
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