Modulation spaces Mp,q for 0<p, q≦∞
The purpose of this paper is to construct modulation spaces Mp,q(Rd) for general 0<p, q≦∞, which coincide with the usual modulation spaces when 1≦p,q≦∞, and study their basic properties including their completeness. Given any g∈S(Rd) such that supp ĝ⊂ {ξ∣|ξ|≦1} and ∑k∈Zdĝ(ξ-αk)≡1, our modula...
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| Format: | Article |
| Language: | English |
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Wiley
2006-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2006/409840 |
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| _version_ | 1832558458361085952 |
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| author | Masaharu Kobayashi |
| author_facet | Masaharu Kobayashi |
| author_sort | Masaharu Kobayashi |
| collection | DOAJ |
| description | The purpose of this paper is to construct modulation spaces Mp,q(Rd) for general 0<p, q≦∞, which coincide with the usual modulation spaces when 1≦p,q≦∞, and study their basic properties including their completeness. Given any g∈S(Rd) such that supp ĝ⊂ {ξ∣|ξ|≦1} and ∑k∈Zdĝ(ξ-αk)≡1, our modulation space consists of all tempered distributions f such that the (quasi)-norm ‖f‖M[g]p,q:≔(∫Rd(∫Rd|f*(Mωg)(x)|pdx)qpdω)1q is finite. |
| format | Article |
| id | doaj-art-7e557738fe6848548481b054ebf64d5c |
| institution | Kabale University |
| issn | 0972-6802 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-7e557738fe6848548481b054ebf64d5c2025-02-03T01:32:17ZengWileyJournal of Function Spaces and Applications0972-68022006-01-014332934110.1155/2006/409840Modulation spaces Mp,q for 0<p, q≦∞Masaharu Kobayashi0Department of Mathematics, Tokyo University of Science, Kagurazaka 1-3, Shinjuku-ku, Tokyo 162-8601, JapanThe purpose of this paper is to construct modulation spaces Mp,q(Rd) for general 0<p, q≦∞, which coincide with the usual modulation spaces when 1≦p,q≦∞, and study their basic properties including their completeness. Given any g∈S(Rd) such that supp ĝ⊂ {ξ∣|ξ|≦1} and ∑k∈Zdĝ(ξ-αk)≡1, our modulation space consists of all tempered distributions f such that the (quasi)-norm ‖f‖M[g]p,q:≔(∫Rd(∫Rd|f*(Mωg)(x)|pdx)qpdω)1q is finite.http://dx.doi.org/10.1155/2006/409840 |
| spellingShingle | Masaharu Kobayashi Modulation spaces Mp,q for 0<p, q≦∞ Journal of Function Spaces and Applications |
| title | Modulation spaces Mp,q for 0<p, q≦∞ |
| title_full | Modulation spaces Mp,q for 0<p, q≦∞ |
| title_fullStr | Modulation spaces Mp,q for 0<p, q≦∞ |
| title_full_unstemmed | Modulation spaces Mp,q for 0<p, q≦∞ |
| title_short | Modulation spaces Mp,q for 0<p, q≦∞ |
| title_sort | modulation spaces mp q for 0 p q≦∞ |
| url | http://dx.doi.org/10.1155/2006/409840 |
| work_keys_str_mv | AT masaharukobayashi modulationspacesmpqfor0pq |