Commutators of Higher Order Riesz Transform Associated with Schrödinger Operators
Let L=-Δ+V be a Schrödinger operator on ℝn (n≥3), where V≢0 is a nonnegative potential belonging to certain reverse Hölder class Bs for s≥n/2. In this paper, we prove the boundedness of commutators ℛbHf=bℛHf-ℛH(bf) generated by the higher order Riesz transform ℛH=∇2(-Δ+V)-1, where b∈BMOθ(ρ), which i...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2013/842375 |
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| author | Yu Liu Lijuan Wang Jianfeng Dong |
| author_facet | Yu Liu Lijuan Wang Jianfeng Dong |
| author_sort | Yu Liu |
| collection | DOAJ |
| description | Let L=-Δ+V be a Schrödinger operator on ℝn (n≥3), where V≢0 is a nonnegative potential belonging to certain reverse Hölder class Bs for s≥n/2. In this paper, we prove the boundedness of commutators ℛbHf=bℛHf-ℛH(bf) generated by the higher order Riesz transform ℛH=∇2(-Δ+V)-1, where b∈BMOθ(ρ), which is larger than the space BMO(ℝn). Moreover, we prove that ℛbH is bounded from the Hardy space HL1(ℝn) into weak Lweak1(ℝn). |
| format | Article |
| id | doaj-art-ae45dbef73524a7f985dfb0e4a7fd062 |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-ae45dbef73524a7f985dfb0e4a7fd0622025-02-03T01:03:49ZengWileyJournal of Function Spaces and Applications0972-68021758-49652013-01-01201310.1155/2013/842375842375Commutators of Higher Order Riesz Transform Associated with Schrödinger OperatorsYu Liu0Lijuan Wang1Jianfeng Dong2School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, ChinaSchool of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, ChinaDepartment of Mathematics, Shanghai University, Shanghai 200444, ChinaLet L=-Δ+V be a Schrödinger operator on ℝn (n≥3), where V≢0 is a nonnegative potential belonging to certain reverse Hölder class Bs for s≥n/2. In this paper, we prove the boundedness of commutators ℛbHf=bℛHf-ℛH(bf) generated by the higher order Riesz transform ℛH=∇2(-Δ+V)-1, where b∈BMOθ(ρ), which is larger than the space BMO(ℝn). Moreover, we prove that ℛbH is bounded from the Hardy space HL1(ℝn) into weak Lweak1(ℝn).http://dx.doi.org/10.1155/2013/842375 |
| spellingShingle | Yu Liu Lijuan Wang Jianfeng Dong Commutators of Higher Order Riesz Transform Associated with Schrödinger Operators Journal of Function Spaces and Applications |
| title | Commutators of Higher Order Riesz Transform Associated with Schrödinger Operators |
| title_full | Commutators of Higher Order Riesz Transform Associated with Schrödinger Operators |
| title_fullStr | Commutators of Higher Order Riesz Transform Associated with Schrödinger Operators |
| title_full_unstemmed | Commutators of Higher Order Riesz Transform Associated with Schrödinger Operators |
| title_short | Commutators of Higher Order Riesz Transform Associated with Schrödinger Operators |
| title_sort | commutators of higher order riesz transform associated with schrodinger operators |
| url | http://dx.doi.org/10.1155/2013/842375 |
| work_keys_str_mv | AT yuliu commutatorsofhigherorderriesztransformassociatedwithschrodingeroperators AT lijuanwang commutatorsofhigherorderriesztransformassociatedwithschrodingeroperators AT jianfengdong commutatorsofhigherorderriesztransformassociatedwithschrodingeroperators |