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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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). |
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| ISSN: | 0972-6802 1758-4965 |