Generalized Carleson Measure Spaces and Their Applications
We introduce the generalized Carleson measure spaces CMOrα,q that extend BMO. Using Frazier and Jawerth's φ-transform and sequence spaces, we show that, for α∈R and 0<p≤1, the duals of homogeneous Triebel-Lizorkin spaces Ḟpα,q for 1<q<∞ and 0<q≤1 are CMO(q'/p)-(q'/q)-α,q&...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/879073 |
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| author | Chin-Cheng Lin Kunchuan Wang |
| author_facet | Chin-Cheng Lin Kunchuan Wang |
| author_sort | Chin-Cheng Lin |
| collection | DOAJ |
| description | We introduce the generalized Carleson measure spaces CMOrα,q that extend BMO. Using Frazier and Jawerth's φ-transform and sequence spaces, we show that, for α∈R and 0<p≤1, the duals of homogeneous Triebel-Lizorkin spaces Ḟpα,q for 1<q<∞ and 0<q≤1 are CMO(q'/p)-(q'/q)-α,q' and CMOr-α+(n/p)-n,∞ (for any r∈R), respectively. As applications, we give the necessary and sufficient conditions for the boundedness of wavelet multipliers and paraproduct operators acting on homogeneous Triebel-Lizorkin spaces. |
| format | Article |
| id | doaj-art-89ea7b79ca1d4a95b6030c5115eb5a5a |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-89ea7b79ca1d4a95b6030c5115eb5a5a2025-02-03T05:52:18ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/879073879073Generalized Carleson Measure Spaces and Their ApplicationsChin-Cheng Lin0Kunchuan Wang1Department of Mathematics, National Central University, Chung-Li 320, TaiwanDepartment of Applied Mathematics, National Dong Hwa University, Hualien 970, TaiwanWe introduce the generalized Carleson measure spaces CMOrα,q that extend BMO. Using Frazier and Jawerth's φ-transform and sequence spaces, we show that, for α∈R and 0<p≤1, the duals of homogeneous Triebel-Lizorkin spaces Ḟpα,q for 1<q<∞ and 0<q≤1 are CMO(q'/p)-(q'/q)-α,q' and CMOr-α+(n/p)-n,∞ (for any r∈R), respectively. As applications, we give the necessary and sufficient conditions for the boundedness of wavelet multipliers and paraproduct operators acting on homogeneous Triebel-Lizorkin spaces.http://dx.doi.org/10.1155/2012/879073 |
| spellingShingle | Chin-Cheng Lin Kunchuan Wang Generalized Carleson Measure Spaces and Their Applications Abstract and Applied Analysis |
| title | Generalized Carleson Measure Spaces and Their Applications |
| title_full | Generalized Carleson Measure Spaces and Their Applications |
| title_fullStr | Generalized Carleson Measure Spaces and Their Applications |
| title_full_unstemmed | Generalized Carleson Measure Spaces and Their Applications |
| title_short | Generalized Carleson Measure Spaces and Their Applications |
| title_sort | generalized carleson measure spaces and their applications |
| url | http://dx.doi.org/10.1155/2012/879073 |
| work_keys_str_mv | AT chinchenglin generalizedcarlesonmeasurespacesandtheirapplications AT kunchuanwang generalizedcarlesonmeasurespacesandtheirapplications |