The Boundedness of Some Integral Operators on Weighted Hardy Spaces Associated with Schrödinger Operators
Let L=-Δ+V be a Schrödinger operator acting on L2(Rn), n≥1, where V≢0 is a nonnegative locally integrable function on Rn. In this paper, we will first define molecules for weighted Hardy spaces HLp(w) (0<p≤1) associated with L and establish their molecular characterizations. Then, by using the a...
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| Format: | Article |
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Wiley
2015-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2015/823862 |
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| author | Hua Wang |
| author_facet | Hua Wang |
| author_sort | Hua Wang |
| collection | DOAJ |
| description | Let L=-Δ+V be a Schrödinger operator acting on L2(Rn), n≥1, where V≢0 is a nonnegative locally integrable function on Rn. In this paper, we will first define molecules for weighted Hardy spaces HLp(w) (0<p≤1) associated with L and establish their molecular characterizations. Then, by using the atomic decomposition and molecular characterization of HLp(w), we will show that the imaginary power Liγ is bounded on HLp(w) for n/(n+1)<p≤1, and the fractional integral operator L-α/2 is bounded from HLp(w) to HLq(wq/p), where 0<α<min{n/2,1}, n/(n+1)<p≤n/(n+α), and 1/q=1/p-α/n. |
| format | Article |
| id | doaj-art-6b08a20821a34c4f843add361516069a |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-6b08a20821a34c4f843add361516069a2025-02-03T01:23:32ZengWileyJournal of Function Spaces2314-88962314-88882015-01-01201510.1155/2015/823862823862The Boundedness of Some Integral Operators on Weighted Hardy Spaces Associated with Schrödinger OperatorsHua Wang0College of Mathematics and Econometrics, Hunan University, Changsha 410082, ChinaLet L=-Δ+V be a Schrödinger operator acting on L2(Rn), n≥1, where V≢0 is a nonnegative locally integrable function on Rn. In this paper, we will first define molecules for weighted Hardy spaces HLp(w) (0<p≤1) associated with L and establish their molecular characterizations. Then, by using the atomic decomposition and molecular characterization of HLp(w), we will show that the imaginary power Liγ is bounded on HLp(w) for n/(n+1)<p≤1, and the fractional integral operator L-α/2 is bounded from HLp(w) to HLq(wq/p), where 0<α<min{n/2,1}, n/(n+1)<p≤n/(n+α), and 1/q=1/p-α/n.http://dx.doi.org/10.1155/2015/823862 |
| spellingShingle | Hua Wang The Boundedness of Some Integral Operators on Weighted Hardy Spaces Associated with Schrödinger Operators Journal of Function Spaces |
| title | The Boundedness of Some Integral Operators on Weighted Hardy Spaces Associated with Schrödinger Operators |
| title_full | The Boundedness of Some Integral Operators on Weighted Hardy Spaces Associated with Schrödinger Operators |
| title_fullStr | The Boundedness of Some Integral Operators on Weighted Hardy Spaces Associated with Schrödinger Operators |
| title_full_unstemmed | The Boundedness of Some Integral Operators on Weighted Hardy Spaces Associated with Schrödinger Operators |
| title_short | The Boundedness of Some Integral Operators on Weighted Hardy Spaces Associated with Schrödinger Operators |
| title_sort | boundedness of some integral operators on weighted hardy spaces associated with schrodinger operators |
| url | http://dx.doi.org/10.1155/2015/823862 |
| work_keys_str_mv | AT huawang theboundednessofsomeintegraloperatorsonweightedhardyspacesassociatedwithschrodingeroperators AT huawang boundednessofsomeintegraloperatorsonweightedhardyspacesassociatedwithschrodingeroperators |