Weighted Herz Spaces and Regularity Results
It is proved that, for the nondivergence form elliptic equations ∑𝑛𝑖,𝑗=1𝑎𝑖𝑗𝑢𝑥𝑖𝑥𝑗=𝑓, if 𝑓 belongs to the weighted Herz spaces 𝐾𝑞𝑝(𝜑,𝑤), then 𝑢𝑥𝑖𝑥𝑗∈𝐾𝑞𝑝(𝜑,𝑤), where 𝑢 is the 𝑊2,𝑝-solution of the equations. In order to obtain this, the authors first establish the weighted boundedness for the commutators...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2012/283730 |
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| author | Yuxing Guo Yinsheng Jiang |
| author_facet | Yuxing Guo Yinsheng Jiang |
| author_sort | Yuxing Guo |
| collection | DOAJ |
| description | It is proved that, for the nondivergence form elliptic equations ∑𝑛𝑖,𝑗=1𝑎𝑖𝑗𝑢𝑥𝑖𝑥𝑗=𝑓, if 𝑓 belongs to the weighted Herz spaces 𝐾𝑞𝑝(𝜑,𝑤), then 𝑢𝑥𝑖𝑥𝑗∈𝐾𝑞𝑝(𝜑,𝑤), where 𝑢 is the 𝑊2,𝑝-solution of the equations. In order to obtain this, the authors first establish the weighted boundedness for the commutators of some singular integral operators on 𝐾𝑞𝑝(𝜑,𝑤). |
| format | Article |
| id | doaj-art-cf3d813ab54543c4a39a1c654bf92771 |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-cf3d813ab54543c4a39a1c654bf927712025-02-03T06:13:58ZengWileyJournal of Function Spaces and Applications0972-68021758-49652012-01-01201210.1155/2012/283730283730Weighted Herz Spaces and Regularity ResultsYuxing Guo0Yinsheng Jiang1College of Mathematics and System Sciences, Xinjiang University, Xinjiang, Urumqi 830046, ChinaCollege of Mathematics and System Sciences, Xinjiang University, Xinjiang, Urumqi 830046, ChinaIt is proved that, for the nondivergence form elliptic equations ∑𝑛𝑖,𝑗=1𝑎𝑖𝑗𝑢𝑥𝑖𝑥𝑗=𝑓, if 𝑓 belongs to the weighted Herz spaces 𝐾𝑞𝑝(𝜑,𝑤), then 𝑢𝑥𝑖𝑥𝑗∈𝐾𝑞𝑝(𝜑,𝑤), where 𝑢 is the 𝑊2,𝑝-solution of the equations. In order to obtain this, the authors first establish the weighted boundedness for the commutators of some singular integral operators on 𝐾𝑞𝑝(𝜑,𝑤).http://dx.doi.org/10.1155/2012/283730 |
| spellingShingle | Yuxing Guo Yinsheng Jiang Weighted Herz Spaces and Regularity Results Journal of Function Spaces and Applications |
| title | Weighted Herz Spaces and Regularity Results |
| title_full | Weighted Herz Spaces and Regularity Results |
| title_fullStr | Weighted Herz Spaces and Regularity Results |
| title_full_unstemmed | Weighted Herz Spaces and Regularity Results |
| title_short | Weighted Herz Spaces and Regularity Results |
| title_sort | weighted herz spaces and regularity results |
| url | http://dx.doi.org/10.1155/2012/283730 |
| work_keys_str_mv | AT yuxingguo weightedherzspacesandregularityresults AT yinshengjiang weightedherzspacesandregularityresults |