Riesz transform on manifolds and Poincaré inequalitie

By P. Auscher, T. Coulhon. 2005

51 citations recorded by the source corpus.

We study the validity of the Lp inequality for the Riesz transform when p > 2 and of its reverse inequality when 1 < p < 2 on complete Riemannian manifolds under the doubling property and some Poincare inequalities. MSC numbers 2000: 58J35, 42B20

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/083669448bea32aca793ad9262be765aaefa3a32

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In Applied Mathematics

1. Renjin Jiang
2. T. Coulhon
3. Adam S. Sikora
4. Pekka Koskela
5. Dachun Yang
6. Xuan Thinh Duong
7. Lixin Yan
8. P. Auscher

In Mathematical Physics

1. Renjin Jiang
2. T. Coulhon
3. Adam S. Sikora
4. Pekka Koskela
5. Dachun Yang
6. Xuan Thinh Duong
7. Andrés Navas
8. P. Auscher

Citations in the corpus

• Gradient estimates for heat kernels and harmonic functions (2017, background): “9 contain three improvements with respect to [6, Theorem 2.1]. First, the proof of [6, Theorem 2.1] makes an essential use of 1-forms on manifolds, and we do not know how to extend the arguments from [6] to our general setting. Second, Theorems 1.6 and 1.9 state a point-to-point equivalence among (R”