| L^p-gradient Estimates of Symmetric Markov Semigroups for 1 〈 p ≤ 2 |
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| 作者姓名： | Ana Bela CRUZEIRO Xi Cheng ZHANG |
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| 作者单位： | [1]Department Matemdtica, I.S.T., Av. Rovisco Pais, 1099-01 Lisboa, Portugal and Grupo de Fisica-Matemdtica, U.L., Lisboa, Portugal [2]Department of Mathematics, Huazhong University of Science and Technology, Wuahan 430074, P. R. China |
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| 基金项目： | The first author is supported by the project P0CTI/MAT/55977/2004 and the second author is supported by NSF （No. 10301011） of China and Project 973 |
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| 摘 要： | For 1 〈 p ≤2, an L^p-gradient estimate for a symmetric Markov semigroup is derived in a general framework, i.e. ‖Γ^/2（Ttf）‖p≤Cp/√t‖p, where F is a carre du champ operator. As a simple application we prove that F1/2（（I- L） ^-α） is a bounded operator from L^p to L^v provided that 1 〈 p 〈 2 and 1/2〈α〈1. For any 1 〈 p 〈 2, q 〉 2 and 1/2 〈α 〈 1, there exist two positive constants cq,α,Cp,α such that ‖Df‖p≤ Cp,α‖（I - L）^αf‖p,Cq,α（I-L）^（1-α）‖Df‖q＋‖f‖q, where D is the Malliavin gradient （[2]） and L the Ornstein-Uhlenbeck operator.
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| 关 键 词： | Markov半群 对称性 路径空间 Malliavin梯度 |
| 收稿时间： | 2003-04-01 |
| 修稿时间： | 2003-04-012004-08-16 |
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