Embeddings of function spaces via the Caffarelli–Silvestre extension, capacities and Wolff potentials
| dc.contributor.author | Li, Pengtao | |
| dc.contributor.author | Shi, Shaoguang | |
| dc.contributor.author | Hu, Rui | |
| dc.contributor.author | Zhai, Zhichun | |
| dc.date.accessioned | 2023-04-21T14:37:03Z | |
| dc.date.available | 2023-04-21T14:37:03Z | |
| dc.date.issued | 2022 | |
| dc.description.abstract | Let Pαf (x, t) be the Caffarelli–Silvestre extension of a smooth function f (x) Rn → Rn+1+ := Rn × (0, ∞). The purpose of this article is twofold. Firstly, we want to characterize a nonnegative measure μ on Rn+1 + such that f (x) → Pαf (x, t) induces bounded embeddings from the Lebesgue spaces Lp(Rn) to the Lq (Rn+1 + , μ). On one hand, these embeddings will be characterized by using a newly introduced Lp−capacity associated with the Caffarelli–Silvestre extension. In doing so, the mixed norm estimates of Pαf (x, t), the dual form of the Lp−capacity, the Lp−capacity of general balls, and a capacitary strong type inequality will be established, respectively. On the other hand, when p > q >1, these embeddings will also be characterized in terms of the Hedberg–Wolff potential of μ. Secondly, we characterize a nonnegative measure μ on Rn+1 + such that f (x) → Pαf (x, t) induces bounded embeddings from the homogeneous Sobolev spaces ̇W β,p(Rn) to the Lq (Rn+1+ , μ) in terms of the fractional perimeter of open sets for endpoint cases and the fractional capacity for general cases. | |
| dc.description.uri | https://library.macewan.ca/cgi-bin/SFX/url.pl/DSG | |
| dc.identifier.citation | Li, P., Shi, S., Hu, R., & Zhai, Z. Embeddings of function spaces via the Caffarelli–Silvestre extension, capacities and Wolff potentials. Nonlinear Analysis, 217, 112758 (2022). https://doi.org/10.1016/j.na.2021.112758 | |
| dc.identifier.doi | https://doi.org/10.1016/j.na.2021.112758 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14078/3072 | |
| dc.language.iso | en | |
| dc.rights | All Rights Reserved | |
| dc.subject | Fractional Laplacian | |
| dc.subject | Lebesgue space | |
| dc.subject | Sobolev space | |
| dc.subject | capacity | |
| dc.subject | fractional perimeter | |
| dc.title | Embeddings of function spaces via the Caffarelli–Silvestre extension, capacities and Wolff potentials | en |
| dc.type | Article |