We prove an abstract form of Hardy's L 2 inequality, in which the Dirichlet integral is replaced by the Dirichlet form of a general symmetric Markov process. A number of examples are provided.
Extremal Functions for Hardy's Inequality with Weight
β Scribed by Haim Brezis; Moshe Marcus; Itai Shafrir
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 157 KB
- Volume
- 171
- Category
- Article
- ISSN
- 0022-1236
No coin nor oath required. For personal study only.
β¦ Synopsis
1 . 3 ) and showed that, for a C 2 bounded domain 0, there exists a finite constant **=**(0) such that { J * =1Γ4, J * <1Γ4, \* **, \*>**.
(1.4)
π SIMILAR VOLUMES
Weighted norm inequalities are investigated by giving an extension of the Riesz convexity theorem to semi-linear operators on monotone functions. Several properties of the classes B@, n) and C(p, n) introduced by NEUGEBAUER in [I31 are given. In particular, we characterize the weight pairs w, v for
We define pluriharmonic conjugate functions on the unit ball of n . Then we show that for a weight there exist weighted norm inequalities for pluriharmonic conjugate functions on L p if and only if the weight satisfies the A p -condition. As an application, we prove the equivalence of the weighted n