On L2-Boundedness of h-Pseudodifferential Operators
Let Tah be the h-pseudodifferential operators with symbol a. When a∈Sρ,1m and m=nρ−1/2, it is well known that Tah is not always bounded in L2ℝn. In this paper, under the condition ax,ξ∈L∞Sρnρ−1/2ω, we show that Tah is bounded on L2.
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/6690963 |
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| _version_ | 1832559758906753024 |
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| author | Jie Yang |
| author_facet | Jie Yang |
| author_sort | Jie Yang |
| collection | DOAJ |
| description | Let Tah be the h-pseudodifferential operators with symbol a. When a∈Sρ,1m and m=nρ−1/2, it is well known that Tah is not always bounded in L2ℝn. In this paper, under the condition ax,ξ∈L∞Sρnρ−1/2ω, we show that Tah is bounded on L2. |
| format | Article |
| id | doaj-art-43dcbdeea7be4fa78a012ed10ad61a37 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-43dcbdeea7be4fa78a012ed10ad61a372025-02-03T01:29:19ZengWileyJournal of Function Spaces2314-88962314-88882021-01-01202110.1155/2021/66909636690963On L2-Boundedness of h-Pseudodifferential OperatorsJie Yang0College of Mathematics and System Science, Xinjiang University, Xinjiang 830046, ChinaLet Tah be the h-pseudodifferential operators with symbol a. When a∈Sρ,1m and m=nρ−1/2, it is well known that Tah is not always bounded in L2ℝn. In this paper, under the condition ax,ξ∈L∞Sρnρ−1/2ω, we show that Tah is bounded on L2.http://dx.doi.org/10.1155/2021/6690963 |
| spellingShingle | Jie Yang On L2-Boundedness of h-Pseudodifferential Operators Journal of Function Spaces |
| title | On L2-Boundedness of h-Pseudodifferential Operators |
| title_full | On L2-Boundedness of h-Pseudodifferential Operators |
| title_fullStr | On L2-Boundedness of h-Pseudodifferential Operators |
| title_full_unstemmed | On L2-Boundedness of h-Pseudodifferential Operators |
| title_short | On L2-Boundedness of h-Pseudodifferential Operators |
| title_sort | on l2 boundedness of h pseudodifferential operators |
| url | http://dx.doi.org/10.1155/2021/6690963 |
| work_keys_str_mv | AT jieyang onl2boundednessofhpseudodifferentialoperators |