Some Weighted Norm Inequalities on Manifolds
| Autor: | Shiliang Zhao |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Applied Mathematics
General Mathematics 010102 general mathematics Poincaré inequality Riemannian manifold Weak type 01 natural sciences Combinatorics symbols.namesake Riesz transform Norm (mathematics) 0103 physical sciences symbols 010307 mathematical physics Nabla symbol 0101 mathematics Mathematics |
| Zdroj: | Chinese Annals of Mathematics, Series B. 39:1001-1016 |
| ISSN: | 1860-6261 0252-9599 |
| Popis: | Let M be a complete non-compact Riemannian manifold satisfying the volume doubling property and the Gaussian upper bounds. Denote by Δ the Laplace-Beltrami operator and by ∇ the Riemannian gradient. In this paper, the author proves the weighted reverse inequality \(\left\| {{\Delta ^{\frac{1}{2}}}f} \right\|_{L^p(w)}\leq C\left\| {|\nabla f|} \right\|_{L^p(w)}\), for some range of p determined by M and w. Moreover, a weak type estimate is proved when p = 1. Some weighted vector-valued inequalities are also established. |
| Databáze: | OpenAIRE |
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