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Comptes Rendus. Mathématique
Functional analysis, Harmonic analysis
Boundedness of second-order Riesz transforms on weighted Hardy and BMO spaces associated with Schrödinger operators
Comptes Rendus. Mathématique, Volume 359 (2021) no. 6, pp. 687-717.

Let d{3,4,5,...} and a weight wA ρ . We consider the second-order Riesz transform T= 2 L -1 associated with the Schrödinger operator L=-Δ+V, where VRH σ with σ>d 2. We present three main results. First T is bounded on the weighted Hardy space H w,L 1 ( d ) associated with L if w enjoys a certain stable property. Secondly T is bounded on the weighted BMO space BMO w,ρ ( d ) associated with L if w also belongs to an appropriate doubling class. Thirdly BMO w,ρ ( d ) is the dual of H w,L 1 ( d ) when wA 1 ρ .

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DOI: https://doi.org/10.5802/crmath.213
Classification: 30H35,  42B20,  42B25,  42B30,  42B37
Trong Nguyen Ngoc 1; Truong Le Xuan 1; Do Tan Duc 1

1. University of Economics Ho Chi Minh City, Vietnam
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     author = {Trong Nguyen Ngoc and Truong Le Xuan and Do Tan Duc},
     title = {Boundedness of second-order {Riesz} transforms on weighted {Hardy} and $BMO$ spaces associated with {Schr\"odinger} operators},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {687--717},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {6},
     year = {2021},
     doi = {10.5802/crmath.213},
     language = {en},
}
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Trong Nguyen Ngoc; Truong Le Xuan; Do Tan Duc. Boundedness of second-order Riesz transforms on weighted Hardy and $BMO$ spaces associated with Schrödinger operators. Comptes Rendus. Mathématique, Volume 359 (2021) no. 6, pp. 687-717. doi : 10.5802/crmath.213. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.213/

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