An Orlicz-Besov Poincaré Inequality via John Domains
Denote by B˙⁎α,ϕ(Ω) the intrinsic Orlicz-Besov space, where α∈R, ϕ is a Young function, and Ω⊂Rn is a domain. For α∈(-n,0) and optimal ϕ, via John domains, we establish criteria for bounded domains Ω⊂Rn supporting an Orlicz-Besov Poincaré inequality. ‖u-uΩ‖Ln/|α|(Ω)≤C‖u‖B˙⁎α,ϕ(Ω) ∀u∈B˙⁎α,ϕ(Ω). This...
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Wiley
2019-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2019/5234507 |
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| author | Hongyan Sun |
| author_facet | Hongyan Sun |
| author_sort | Hongyan Sun |
| collection | DOAJ |
| description | Denote by B˙⁎α,ϕ(Ω) the intrinsic Orlicz-Besov space, where α∈R, ϕ is a Young function, and Ω⊂Rn is a domain. For α∈(-n,0) and optimal ϕ, via John domains, we establish criteria for bounded domains Ω⊂Rn supporting an Orlicz-Besov Poincaré inequality. ‖u-uΩ‖Ln/|α|(Ω)≤C‖u‖B˙⁎α,ϕ(Ω) ∀u∈B˙⁎α,ϕ(Ω). This extends the known criteria for bounded domains supporting Sobolev-Poincaré inequality and its fractional analogue. |
| format | Article |
| id | doaj-art-daf2bc7b99c04540a520931ccc39b1b4 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-daf2bc7b99c04540a520931ccc39b1b42025-02-03T01:33:08ZengWileyJournal of Function Spaces2314-88962314-88882019-01-01201910.1155/2019/52345075234507An Orlicz-Besov Poincaré Inequality via John DomainsHongyan Sun0Department of Sciences, China University of Geosciences, Beijing 100083, ChinaDenote by B˙⁎α,ϕ(Ω) the intrinsic Orlicz-Besov space, where α∈R, ϕ is a Young function, and Ω⊂Rn is a domain. For α∈(-n,0) and optimal ϕ, via John domains, we establish criteria for bounded domains Ω⊂Rn supporting an Orlicz-Besov Poincaré inequality. ‖u-uΩ‖Ln/|α|(Ω)≤C‖u‖B˙⁎α,ϕ(Ω) ∀u∈B˙⁎α,ϕ(Ω). This extends the known criteria for bounded domains supporting Sobolev-Poincaré inequality and its fractional analogue.http://dx.doi.org/10.1155/2019/5234507 |
| spellingShingle | Hongyan Sun An Orlicz-Besov Poincaré Inequality via John Domains Journal of Function Spaces |
| title | An Orlicz-Besov Poincaré Inequality via John Domains |
| title_full | An Orlicz-Besov Poincaré Inequality via John Domains |
| title_fullStr | An Orlicz-Besov Poincaré Inequality via John Domains |
| title_full_unstemmed | An Orlicz-Besov Poincaré Inequality via John Domains |
| title_short | An Orlicz-Besov Poincaré Inequality via John Domains |
| title_sort | orlicz besov poincare inequality via john domains |
| url | http://dx.doi.org/10.1155/2019/5234507 |
| work_keys_str_mv | AT hongyansun anorliczbesovpoincareinequalityviajohndomains AT hongyansun orliczbesovpoincareinequalityviajohndomains |