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

1 University of Economics Ho Chi Minh City, Vietnam
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     title = {Boundedness of second-order {Riesz} transforms on weighted {Hardy} and $BMO$ spaces associated with {Schr\"odinger} operators},
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Nguyen Ngoc, Trong; Le Xuan, Truong; Tan Duc, Do. 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. http://www.numdam.org/articles/10.5802/crmath.213/

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