Toward Weighted Lorentz–Sobolev Capacities from Caffarelli–Silvestre Extensions
- Resource Type
- Original Paper
- Authors
- Fu, Xing; Xiao, Jie; Xiong, Qi
- Source
- The Journal of Geometric Analysis. 34(5)
- Subject
- Weighted Lorentz–Sobolev space
Capacity
Embedding
Caffarelli–Silvestre Extension
Primary 31C15
Secondary 46E30
46E35
42B37
- Language
- English
- ISSN
- 1050-6926
1559-002X
Getting inspired by the Caffarelli–Silvestre extensions, this paper investigates the weighted Lorentz–Sobolev capacities and their capacitary strong inequalities with applications to the Sobolev-type embeddings. Consequently, the weighted Lebesgue-Sobolev capacities and their applications to a functional inequality problem and the existence-regularity of solutions to the prototype p-Laplace equations with weight are addressed as well.