The Higher Order Riesz Transform and BMO Type Space Associated with Schrödinger Operators on Stratified Lie Groups
Assume that G is a stratified Lie group and Q is the homogeneous dimension of G. Let -Δ be the sub-Laplacian on G and W≢0 a nonnegative potential belonging to certain reverse Hölder class Bs for s≥Q/2. Let L=-Δ+W be a Schrödinger operator on the stratified Lie group G. In this paper, we prove the bo...
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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/10.1155/2013/483951 |
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| _version_ | 1832553933765083136 |
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| author | Yu Liu Jianfeng Dong |
| author_facet | Yu Liu Jianfeng Dong |
| author_sort | Yu Liu |
| collection | DOAJ |
| description | Assume that G is a stratified Lie group and Q is the homogeneous dimension of G. Let -Δ be the sub-Laplacian on G and W≢0 a nonnegative potential belonging to certain reverse Hölder class Bs for s≥Q/2. Let L=-Δ+W be a Schrödinger operator on the stratified Lie group G. In this paper, we prove the boundedness of some integral operators related to L, such as L-1∇2, L-1W, and L-1(-Δ) on the space BMOL(G). |
| format | Article |
| id | doaj-art-2f58863b4c9c46b5accf045a7274e558 |
| 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-2f58863b4c9c46b5accf045a7274e5582025-02-03T05:52:41ZengWileyJournal of Function Spaces and Applications0972-68021758-49652013-01-01201310.1155/2013/483951483951The Higher Order Riesz Transform and BMO Type Space Associated with Schrödinger Operators on Stratified Lie GroupsYu Liu0Jianfeng Dong1School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, ChinaDepartment of Mathematics, Shanghai University, Shanghai 200444, ChinaAssume that G is a stratified Lie group and Q is the homogeneous dimension of G. Let -Δ be the sub-Laplacian on G and W≢0 a nonnegative potential belonging to certain reverse Hölder class Bs for s≥Q/2. Let L=-Δ+W be a Schrödinger operator on the stratified Lie group G. In this paper, we prove the boundedness of some integral operators related to L, such as L-1∇2, L-1W, and L-1(-Δ) on the space BMOL(G).http://dx.doi.org/10.1155/2013/483951 |
| spellingShingle | Yu Liu Jianfeng Dong The Higher Order Riesz Transform and BMO Type Space Associated with Schrödinger Operators on Stratified Lie Groups Journal of Function Spaces and Applications |
| title | The Higher Order Riesz Transform and BMO Type Space Associated with Schrödinger Operators on Stratified Lie Groups |
| title_full | The Higher Order Riesz Transform and BMO Type Space Associated with Schrödinger Operators on Stratified Lie Groups |
| title_fullStr | The Higher Order Riesz Transform and BMO Type Space Associated with Schrödinger Operators on Stratified Lie Groups |
| title_full_unstemmed | The Higher Order Riesz Transform and BMO Type Space Associated with Schrödinger Operators on Stratified Lie Groups |
| title_short | The Higher Order Riesz Transform and BMO Type Space Associated with Schrödinger Operators on Stratified Lie Groups |
| title_sort | higher order riesz transform and bmo type space associated with schrodinger operators on stratified lie groups |
| url | http://dx.doi.org/10.1155/2013/483951 |
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