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Dowling, Thomas and O'Farrell, Anthony G. (1997) Sobolev Space Analytic Capacities. The Mathematical Proceedings of the Royal Irish Academy, section A, 97A (1). pp. 87-99.
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Abstract
Analytic capacities are set functions defined on the family of compact subsets of the plane which may be used in the study of removable singularities, boundary smoothness, and approximation of analytic functions. The purpose of the present paper is to investigate the analytic capacities associated to Sobolev spaces. For technical reasons, we do not work with the usual Sobolev spaces W k,p. Instead, we work with locally-equivalent spaces, denoted W k,p ∞. We denote the∂-W k,p ∞-cap by γ k,p , and we abbreviate γ 1,p to γ p. We denote the area of the set E by |E|. For each p ∈ [1, ∞], the null-sets of γ p are precisely the sets of zero area. For 1 1 such that
| Item Type: | Article |
|---|---|
| Keywords: | Sobolev; Space; Analytic; Capacities; |
| Academic Unit: | Faculty of Science and Engineering > Computer Science |
| Item ID: | 20906 |
| Identification Number: | 10.2307/20490232 |
| Depositing User: | IR Editor |
| Date Deposited: | 10 Dec 2025 11:27 |
| Journal or Publication Title: | The Mathematical Proceedings of the Royal Irish Academy, section A |
| Publisher: | Royal Irish Academy |
| Refereed: | Yes |
| Related URLs: | |
| Use Licence: | This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here |
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