Inclusions of Hardy Orlicz spaces
Let ϕ be a continuous positive increasing function defined on [0,∞) such that ϕ(x+y)≤ϕ(x)+ϕ(y) and ϕ(0)=0. The Hardy-Orlicz space generated by ϕ is denoted by H(ϕ). In this paper, we prove that for ϕ≠ψ, if H(ϕ)=H(ψ) as sets, then H(ϕ)=H(ψ) as topological vector spaces. Some other results are given....
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| Format: | Article |
| Language: | English |
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Wiley
1986-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171286000558 |
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| _version_ | 1832560915877199872 |
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| author | Roshdi Khalil |
| author_facet | Roshdi Khalil |
| author_sort | Roshdi Khalil |
| collection | DOAJ |
| description | Let ϕ be a continuous positive increasing function defined on [0,∞) such that ϕ(x+y)≤ϕ(x)+ϕ(y) and ϕ(0)=0. The Hardy-Orlicz space generated by ϕ is denoted by H(ϕ). In this paper, we prove that for ϕ≠ψ, if H(ϕ)=H(ψ) as sets, then H(ϕ)=H(ψ) as topological vector spaces. Some other results are given. |
| format | Article |
| id | doaj-art-f8f4e75d4b714bf3b8bd5082e9e32719 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1986-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-f8f4e75d4b714bf3b8bd5082e9e327192025-02-03T01:26:31ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251986-01-019342943410.1155/S0161171286000558Inclusions of Hardy Orlicz spacesRoshdi Khalil0Department of Mathematics, The University of Michigan, Ann Arbor 48109, Michigan, USALet ϕ be a continuous positive increasing function defined on [0,∞) such that ϕ(x+y)≤ϕ(x)+ϕ(y) and ϕ(0)=0. The Hardy-Orlicz space generated by ϕ is denoted by H(ϕ). In this paper, we prove that for ϕ≠ψ, if H(ϕ)=H(ψ) as sets, then H(ϕ)=H(ψ) as topological vector spaces. Some other results are given.http://dx.doi.org/10.1155/S0161171286000558modulus functionOrlicz spaces. |
| spellingShingle | Roshdi Khalil Inclusions of Hardy Orlicz spaces International Journal of Mathematics and Mathematical Sciences modulus function Orlicz spaces. |
| title | Inclusions of Hardy Orlicz spaces |
| title_full | Inclusions of Hardy Orlicz spaces |
| title_fullStr | Inclusions of Hardy Orlicz spaces |
| title_full_unstemmed | Inclusions of Hardy Orlicz spaces |
| title_short | Inclusions of Hardy Orlicz spaces |
| title_sort | inclusions of hardy orlicz spaces |
| topic | modulus function Orlicz spaces. |
| url | http://dx.doi.org/10.1155/S0161171286000558 |
| work_keys_str_mv | AT roshdikhalil inclusionsofhardyorliczspaces |